# SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board 2021 chapter 5 - Co-ordinate Geometry [Latest edition]

#### Chapters ## 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
Q.1 (A)

### SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board 2021 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 2021 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 2021 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 2021 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 2021 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 2021 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 2021 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 2021 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.

## 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 2021 chapter 5 - Co-ordinate Geometry

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Concepts covered in 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board 2021 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.

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