ICSE Class 10th Mathematics Chapter 13 - Section and Mid Point Formula Important Questions with Answers

P is a point on the line joining A(4, 3) and B(–2, 6) such that 5AP = 2BP. Find the co-ordinates of P.

Calculate the ratio in which the line joining the points (–3, –1) and (5, 7) is divided by the line x = 2. Also, find the co-ordinates of the point of intersection.

Calculate the ratio in which the line joining A(6, 5) and B(4, –3) is divided by the line y = 2.

The point P (5, – 4) divides the line segment AB, as shown in the figure, in the ratio 2 : 5. Find the co-ordinates of points A and B. Given AP is smaller than BP.

Find the co-ordinates of the points of tri-section of the line joining the points (–3, 0) and (6, 6).

Show that the line segment joining the points (–5, 8) and (10, ?4) is trisected by the co-ordinate axes.

Show that A (3, –2) is a point of trisection of the line segment joining the points (2, 1) and (5, ?8). Also, find the co-ordinates of the other point of trisection.

If A = (?4, 3) and B = (8, ?6)

1. Find the length of AB.
2. In what ratio is the line joining A and B, divided by the x-axis?

The line segment joining the points M(5, 7) and N(–3, 2) is intersected by the y-axis at point L. Write down the abscissa of L. Hence, find the ratio in which L divides MN. Also, find the co-ordinates of L.

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

1. Calculate the co-ordinates of P and Q.
2. Show that : `PQ = 1/3 BC`.