SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board chapter 5 - Co-ordinate Geometry [Latest edition]

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SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board chapter 5 - Co-ordinate Geometry - Shaalaa.com
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Solutions for Chapter 5: Co-ordinate Geometry

Below listed, you can find solutions for Chapter 5 of Maharashtra State Board SCERT Maharashtra Question Bank for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board.


Q.1 (A)Q.1 (B)Q.2 (A)Q.2 (B)Q.3 (A)Q.3 (B)Q.4Q.5
Q.1 (A)

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Chapter 5 Co-ordinate Geometry Q.1 (A)

MCQ [1 Mark]

Q.1 (A) | Q 1

Point P is midpoint of segment AB where A(– 4, 2) and B(6, 2), then the coordinates of P are ______

  • (–1, 2)

  • (1, 2)

  • (1, –2)

  • (–1, 2)

Q.1 (A) | Q 2

The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x ______

  • 2

  • 6

  • 3

  • 1

Q.1 (A) | Q 3

The distance between points P(–1, 1) and Q(5, –7) is ______

  • 11 cm

  • 10 cm

  • 5 cm

  • 7 cm

Q.1 (A) | Q 4

If the length of the segment joining point L(x, 7) and point M(1, 15) is 10 cm, then the value of x is ______

  • 7

  • 7 or – 5

  • –1

  • 1

Q.1 (A) | Q 5

Find distance between point A(– 3, 4) and origin O

  • 7 cm

  • 10 cm

  • 5 cm

  • – 5cm

Q.1 (A) | Q 6

If point P(1, 1) divide segment joining point A and point B(–1, –1) in the ratio 5 : 2, then the coordinates of A are ______

  • (3, 3)

  • (6, 6)

  • (2, 2)

  • (1, 1)

Q.1 (A) | Q 7

If segment AB is parallel Y-axis and coordinates of A are (1, 3), then the coordinates of B are ______

  • (3, 1)

  • (5, 3)

  • (3, 0)

  • (1, – 3)

Q.1 (A) | Q 8

If point P is midpoint of segment joining point A(– 4, 2) and point B(6, 2), then the coordinates of P are ______

  • (–1, 2)

  • (1, 2)

  • (1, –2)

  • (–1, –2)

Q.1 (A) | Q 9

If point P divides segment AB in the ratio 1 : 3 where A(– 5, 3) and B(3, – 5), then the coordinates of P are ______

  • (– 2, – 2)

  • (– 1, – 1)

  • (– 3, 1)

  • (1, – 3)

Q.1 (A) | Q 10

If the sum of X-coordinates of the vertices of a triangle is 12 and the sum of Y-coordinates is 9, then the coordinates of centroid are ______

  • (12, 9)

  • (9, 12)

  • (4, 3)

  • (3, 4)

Q.1 (B)

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Chapter 5 Co-ordinate Geometry Q.1 (B)

Solve the following [1 Mark]

Q.1 (B) | Q 1

Find the coordinates of the point of intersection of the graph of the equation x = 2 and y = – 3

Q.1 (B) | Q 2

Find distance between point A(7, 5) and B(2, 5)

Q.1 (B) | Q 3

The coordinates of diameter AB of a circle are A(2, 7) and B(4, 5), then find the coordinates of the centre

Q.1 (B) | Q 4

Write the X-coordinate and Y-coordinate of point P(– 5, 4)

Q.1 (B) | Q 5

What are the coordinates of origin?

Q.1 (B) | Q 6

Find distance of point A(6, 8) from origin

Q.1 (B) | Q 7

Find coordinates of midpoint of segment joining (– 2, 6) and (8, 2)

Q.1 (B) | Q 8

Find the coordinates of centroid of a triangle whose vertices are (4, 7), (8, 4) and (7, 11)

Q.1 (B) | Q 9

Find distance between points O(0, 0) and B(– 5, 12)

Q.1 (B) | Q 10

Find coordinates of midpoint of the segment joining points (0, 2) and (12, 14)

Q.2 (A)

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Chapter 5 Co-ordinate Geometry Q.2 (A)

Complete the activity [2 Marks]

Q.2 (A) | Q 1

Find distance between point Q(3, – 7) and point R(3, 3)

Solution: Suppose Q(x1, y1) and point R(x2, y2)

x1 = 3, y1 = – 7 and x2 = 3, y2 = 3

Using distance formula,

d(Q, R) = `sqrt(square)`

∴ d(Q, R) = `sqrt(square - 100)`

∴ d(Q, R) =  `sqrt(square)`

∴ d(Q, R) = `square`

Q.2 (A) | Q 2

Find distance between point A(–1, 1) and point B(5, –7):

Solution: Suppose A(x1, y1) and B(x2, y2)

x1 = –1, y1 = 1 and x2 = 5, y2 = – 7

Using distance formula,

d(A, B) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

∴ d(A, B) = `sqrt(square +[(-7) + square]^2`

∴ d(A, B) = `sqrt(square)`

∴ d(A, B) = `square`

Q.2 (A) | Q 3

Find coordinates of the midpoint of a segment joining point A(–1, 1) and point B(5, –7)

Solution: Suppose A(x1, y1) and B(x2, y2)

x1 = –1, y1 = 1 and x2 = 5, y2 = –7

Using midpoint formula,

∴ Coordinates of midpoint of segment AB 

= `((x_1 + x_2)/2, (y_1+ y_2)/2)`

= `(square/2, square/2)`

∴ Coordinates of the midpoint = `(4/2, square/2)`

∴ Coordinates of the midpoint = `(2, square)`

Q.2 (A) | Q 4

The coordinates of the vertices of a triangle ABC are A (–7, 6), B(2, –2) and C(8, 5). Find coordinates of its centroid.

Solution: Suppose A(x1, y1) and B(x2, y2) and C(x3, y3)

 x1 = –7, y1 = 6 and x2 = 2, y2 = –2 and x3 = 8, y3 = 5

Using Centroid formula

∴ Coordinates of the centroid of a traingle

ABC = `((x_1 + x_2 + x_3)/3, (y_1 + y_2 + y_3)/3)`

= `(square/3, square/3)`

∴ Coordinates of the centroid of a triangle ABC = `(3/3, square)`

∴ Coordinates of the centroid of a triangle ABC = `(1 , square)`

Q.2 (B)

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Chapter 5 Co-ordinate Geometry Q.2 (B)

Solve [2 Marks]

Q.2 (B) | Q 1

The point Q divides segment joining A(3, 5) and B(7, 9) in the ratio 2 : 3. Find the X-coordinate of Q

Q.2 (B) | Q 2

If the distance between point L(x, 7) and point M(1, 15) is 10, then find the value of x

Q.2 (B) | Q 3

Find the coordinates of midpoint of segment joining (22, 20) and (0, 16)

Q.2 (B) | Q 4

Find distance CD where C(– 3a, a), D(a, – 2a)

Q.2 (B) | Q 5

Show that the point (11, – 2) is equidistant from (4, – 3) and (6, 3)

Q.3 (A)

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Chapter 5 Co-ordinate Geometry Q.3 (A)

Complete the activity [3 Marks]

Q.3 (A) | Q 1

If the point P (6, 7) divides the segment joining A(8, 9) and B(1, 2) in some ratio, find that ratio

Solution:

Point P divides segment AB in the ratio m: n.

A(8, 9) = (x1, y1), B(1, 2 ) = (x2, y2) and P(6, 7) = (x, y)

Using Section formula of internal division,

∴ 7 = `("m"(square) - "n"(9))/("m" + "n")`

∴ 7m + 7n = `square` + 9n

∴ 7m – `square` = 9n – `square`

∴ `square` = 2n

∴ `"m"/"n" = square`

Q.3 (A) | Q 2

From the figure given alongside, find the length of the median AD of triangle ABC. Complete the activity.


Solution:

Here A(–1, 1), B(5, – 3), C(3, 5) and suppose D(x, y) are coordinates of point D.

Using midpoint formula,

x = `(5 + 3)/2`

∴ x = `square`

y = `(-3 + 5)/2`

∴ y = `square`

Using distance formula,

∴ AD = `sqrt((4 - square)^2 + (1 - 1)^2`

∴ AD = `sqrt((square)^2 + (0)^2`

∴ AD = `sqrt(square)`

∴ The length of median AD = `square`

Q.3 (B)

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Chapter 5 Co-ordinate Geometry Q.3 (B)

Solve the following [3 Marks]

Q.3 (B) | Q 1

Show that P(– 2, 2), Q(2, 2) and R(2, 7) are vertices of a right angled triangle

Q.3 (B) | Q 2

Show that the point (0, 9) is equidistant from the points (– 4, 1) and (4, 1)

Q.3 (B) | Q 3

Point P(– 4, 6) divides point A(– 6, 10) and B(m, n) in the ratio 2:1, then find the coordinates of point B

Q.4

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Chapter 5 Co-ordinate Geometry Q.4

Solve [4 Marks]

Q.4 | Q 1

Show that points A(– 4, –7), B(–1, 2), C(8, 5) and D(5, – 4) are the vertices of a parallelogram ABCD

Q.4 | Q 2

Show that the points (0, –1), (8, 3), (6, 7) and (– 2, 3) are vertices of a rectangle.

Q.4 | Q 3

Show that the points (2, 0), (– 2, 0) and (0, 2) are vertices of a triangle. State the type of triangle with reason

Q.4 | Q 4

If A(5, 4), B(–3, –2) and C(1, –8) are the vertices of a ∆ABC. Segment AD is median. Find the length of seg AD:

Q.4 | Q 5

Show that A(1, 2), (1, 6), C(1 + 2 `sqrt(3)`, 4) are vertices of a equilateral triangle

Q.5

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Chapter 5 Co-ordinate Geometry Q.5

Solve [3 Marks]

Q.5 | Q 1

Seg OA is the radius of a circle with centre O. The coordinates of point A is (0, 2) then decide whether the point B(1, 2) is on the circle?

Q.5 | Q 2

Find the ratio in which Y-axis divides the point A(3, 5) and point B(– 6, 7). Find the coordinates of the point

Q.5 | Q 3

The points (7, – 6), (2, k) and (h, 18) are the vertices of triangle. If (1, 5) are the coordinates of centroid, find the value of h and k

Q.5 | Q 4

Using distance formula decide whether the points (4, 3), (5, 1), and (1, 9) are collinear or not.

Solutions for Chapter 5: Co-ordinate Geometry

Q.1 (A)Q.1 (B)Q.2 (A)Q.2 (B)Q.3 (A)Q.3 (B)Q.4Q.5
SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board chapter 5 - Co-ordinate Geometry - Shaalaa.com

SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board chapter 5 - Co-ordinate Geometry

Shaalaa.com has the Maharashtra State Board Mathematics 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. SCERT Maharashtra Question Bank solutions for Mathematics 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Maharashtra State Board 5 (Co-ordinate Geometry) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

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Concepts covered in 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board chapter 5 Co-ordinate Geometry are Distance Formula, Division of a Line Segment, Coordinate Geometry, Intercepts Made by a Line, Slope of a Line, General Equation of a Line, Standard Forms of Equation of a Line, The Mid-point of a Line Segment (Mid-point Formula), Section Formula, Centroid Formula.

Using SCERT Maharashtra Question Bank 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board solutions Co-ordinate Geometry exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in SCERT Maharashtra Question Bank Solutions are essential questions that can be asked in the final exam. Maximum Maharashtra State Board 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board students prefer SCERT Maharashtra Question Bank Textbook Solutions to score more in exams.

Get the free view of Chapter 5, Co-ordinate Geometry 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board additional questions for Mathematics 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board Maharashtra State Board, and you can use Shaalaa.com to keep it handy for your exam preparation.

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