M l aggarwal understanding icse mathematics class 10 Solutions for Chapter 10 section formula

Exercises in Chapter 10 section formula Grade 10

Section Formula Exercise 11

Questions in Section Formula Exercise 11

Find the coordinates of the point which is three-fourth of the way from A (3, 1) to B ( – 2, 5).

P divides the distance between A ( – 2, 1) and B (1, 4) in the ratio of 2 : 1. Calculate the co-ordinates of the point P.

Find the co-ordinates of the points of trisection of the line segment joining the point (3, – 3) and (6, 9).

The line segment joining the points (3, – 4) and (1, 2) is trisected at the points P and Q. If the coordinates of P and Q are (p, – 2) and (5/3, q) respectively, find the values of p and q.

Find the co-ordinates of the mid-point of the line segments joining the following pairs of points:

(2, – 3), ( – 6, 7)

Find the co-ordinates of the mid-point of the line segments joining the following pairs of points:

(5, – 11), (4, 3)

Find the co-ordinates of the mid-point of the line segments joining the following pairs of points:

(a + 3, 5b), (2a – 1, 3b + 4)

A point P divides the line segment joining the points A (3, – 5) and B ( – 4, 8) such that AP/PB = k/1 If P lies on the line x + y = 0, then find the value of k.

The line segment joining the points A (3, 2) and B (5, 1) is divided at the point P in the ratio 1 : 2 and it lies on the line 3x – 18y + k = 0. Find the value of k.

Point P (3, – 5) is reflected to P’ in the x- axis. Also P on reflection in the y-axis is mapped as P”.

Find the co-ordinates of P’ and P”.

Point P (3, – 5) is reflected to P’ in the x- axis. Also P on reflection in the y-axis is mapped as P”.

Compute the distance P’ P”.

Point P (3, – 5) is reflected to P’ in the x- axis. Also P on reflection in the y-axis is mapped as P”.

Find the middle point of the line segment P’ P”.

Point P (3, – 5) is reflected to P’ in the x- axis. Also P on reflection in the y-axis is mapped as P”.

On which co-ordinate axis does the middle point of the line segment P P” lie ?

Use graph paper for this question. Take 1 cm = 1 unit on both axes. Plot the points A(3, 0) and B(0, 4).

Write down the co-ordinates of A1, the reflection of A in the y-axis.

Use graph paper for this question. Take 1 cm = 1 unit on both axes. Plot the points A(3, 0) and B(0, 4).

Write down the co-ordinates of B1, the reflection of B in the x-axis.

Use graph paper for this question. Take 1 cm = 1 unit on both axes. Plot the points A(3, 0) and B(0, 4).

Assign the special name to the quadrilateral ABA1B1.

The mid-point of the line segment AB shown in the adjoining diagram is (4, – 3). Write down the co-ordinates of A and B.

Use graph paper for this question. Take 1 cm = 1 unit on both axes. Plot the points A(3, 0) and B(0, 4).

Assign the special name to quadrilateral ABC1B1.

The line segment joining A ( – 3, 1) and B (5, – 4) is a diameter of a circle whose centre is C.

find the co-ordinates of the point C.

The mid-point of the line segment joining the points (3m, 6) and ( – 4, 3n) is (1, 2m – 1).

Find the values of m and n.

The co-ordinates of the mid-point of the line segment PQ are (1, – 2). The co-ordinates of P are ( – 3, 2).

Find the co-ordinates of Q.

AB is a diameter of a circle with centre C ( – 2, 5). If point A is (3, – 7).

Find: the length of radius AC.

AB is a diameter of a circle with centre C ( – 2, 5). If point A is (3, – 7).

Find: the coordinates of B.

Find the reflection (image) of the point (5, – 3) in the point ( – 1, 3).

The line segment joining A(-1,5/3) the points B (a, 5) is divided in the ratio 1 : 3 at P, the point where the line segment AB intersects y-axis.

Calculate the value of a.

Calculate the length of the median through the vertex A of the triangle ABC with vertices A (7, – 3), B (5, 3) and C (3, – 1).

The vertices of a triangle are A ( – 5, 3), B (p, – 1) and C (6, q). Find the values of p and q if the centroid of the triangle ABC is the point (1, – 1).

The line segment joining A(-1,5/3) the points B (a, 5) is divided in the ratio 1 : 3 at P, the point where the line segment AB intersects y-axis.

Calculate the co-ordinates of P.

The point P ( – 4, 1) divides the line segment joining the points A (2, – 2) and B in the ratio of 3 : 5.

Find the point B.

In what ratio does the point (5, 4) divide the line segment joining the points (2, 1) and (7 ,6) ?

The line segment joining A (2, 3) and B (6, – 5) is intercepted by the x-axis at the point K. Write the ordinate of the point k. Hence, find the ratio in which K divides AB. Also, find the coordinates of the point K.

If A ( – 4, 3) and B (8, – 6), find the length of AB.

Calculate the ratio in which the line segment joining (3, 4) and( – 2, 1) is divided by the y-axis.

In what ratio does the line x – y – 2 = 0 divide the line segment joining the points (3, – 1) and (8, 9)? Also, find the coordinates of the point of division.

Given a line segment AB joining the points A ( – 4, 6) and B (8, – 3).

Find: the ratio in which AB is divided by the y-axis.

Given a line segment AB joining the points A ( – 4, 6) and B (8, – 3).

Find: the coordinates of the point of intersection.

Write down the co-ordinates of the point P that divides the line joining A ( – 4, 1) and B (17,10) in the ratio 1 : 2.

Given a line segment AB joining the points A ( – 4, 6) and B (8, – 3).

Find: the length of AB.

In what ratio does the y-axis divide the line AB ?

Calculate the distance OP where O is the origin.

A (2, 5), B ( – 1, 2) and C (5, 8) are the vertices of a triangle ABC. P and Q are points on AB and AC respectively such that AP : PB = AQ : QC = 1 : 2.

Find the co-ordinates of P and Q.

Use graph paper for this question. Take 1 cm = 1 unit on both axes. Plot the points A(3, 0) and B(0, 4).

If C is the midpoint is AB. Write down the co-ordinates of the point C1, the reflection of C in the origin.

Find the third vertex of a triangle if its two vertices are ( – 1, 4) and (5, 2) and midpoint of one sides is (0, 3).

If the points A ( – 2, – 1), B (1, 0), C (p, 3) and D (1, q) form a parallelogram ABCD, find the values of p and q.

If two vertices of a parallelogram are (3, 2) ( – 1, 0) and its diagonals meet at (2, – 5), find the other two vertices of the parallelogram

Find the coordinates of the vertices of the triangle the middle points of whose sides are $\left(0, \frac{1}{2}\right) , \left( \frac{1}{2} , \frac{1}{2}\right)\text{ and }\left( \frac{1}{2}, 0\right)$ .

Find the value of p for which the points ( – 5, 1), (1, p) and (4, – 2) are collinear.

Show by section formula that the points (3, – 2), (5, 2) and (8, 8) are collinear.

A (10, 5), B (6, – 3) and C (2, 1) are the vertices of triangle ABC. L is the mid point of AB, M is the mid-point of AC.

Write down the co-ordinates of L and M. Show that LM = $\frac{1}{2}$ BC.

If A ( – 4, 3) and B (8, – 6), in what ratio is the line joining AB, divided by the x-axis

A (2, 5), B ( – 1, 2) and C (5, 8) are the vertices of a triangle ABC. P and Q are points on AB and AC respectively such that AP : PB = AQ : QC = 1 : 2.

Show that PQ = 1/3 BC

In what ratio does the point ( – 4, b) divide the line segment joining the points P (2, – 2), Q ( – 14, 6) ?

Hence find the value of b.

Two vertices of a triangle are (3, – 5) and ( – 7, 4). Find the third vertex given that the centroid is (2, – 1).

Find the co-ordinates of the centroid of a triangle whose vertices are A ( – 1, 3), B(1, – 1) and C (5, 1)

Three consecutive vertices of a parallelogram ABCD are A (1, 2), B (1, 0) and C (4, 0).

Find the fourth vertex D.

The co-ordinates of two points A and B are ( – 3, 3) and (12, – 7) respectively. P is a point on the line segment AB such that AP : PB = 2 : 3.

Find the co-ordinates of P.

Prove that the points A ( – 5, 4), B ( – 1, – 2) and C (5, 2) are the vertices of an isosceles right angled triangle.

Find the co-ordinates of D so that ABCD is a square.