#### Chapters

Chapter 2: Pythagoras Theorem

Chapter 3: Circle

Chapter 4: Geometric Constructions

Chapter 5: Co-ordinate Geometry

Chapter 6: Trigonometry

## Chapter 5: Co-ordinate Geometry

### 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]

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)

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

2

6

3

1

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

11 cm

10 cm

5 cm

7 cm

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

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

7 cm

10 cm

5 cm

– 5cm

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)

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)

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)

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)

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)

### 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]

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

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

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

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

What are the coordinates of origin?

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

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

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

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

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

### 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]

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

**Solution:** Suppose Q(x_{1}, y_{1}) and point R(x_{2}, y_{2})

x_{1} = 3, y_{1} = – 7 and x_{2} = 3, y_{2} = 3

Using distance formula,

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

∴ d(Q, R) = `sqrt(square - 100)`

∴ d(Q, R) = `sqrt(square)`

∴ d(Q, R) = `square`

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

**Solution:** Suppose A(x_{1}, y_{1}) and B(x_{2}, y_{2})

x_{1} = –1, y_{1} = 1 and x_{2} = 5, y_{2} = – 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`

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

**Solution:** Suppose A(x_{1}, y_{1}) and B(x_{2}, y_{2})

x_{1} = –1, y_{1} = 1 and x_{2} = 5, y_{2} = –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)`

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(x_{1}, y_{1}) and B(x_{2}, y_{2}) and C(x_{3}, y_{3})

x_{1} = –7, y_{1} = 6 and x_{2} = 2, y_{2} = –2 and x_{3} = 8, y_{3} = 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)`

### 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]

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

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

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

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

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

### 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]

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) = (x_{1}, y_{1}), B(1, 2 ) = (x_{2}, y_{2}) 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`

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`

### 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]

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

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

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

### 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]

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

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

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

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:

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

### 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]

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?

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

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

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

## Chapter 5: Co-ordinate Geometry

## 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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