NCERT Class 10 Mathematics

172 MATHEMATICS

(v) If A(x 1 , y 1 ), B(x 2 , y 2 ) and C(x 3 , y 3 ) are the vertices of  ABC, find the coordinates of

the centroid of the triangle.

8. ABCD is a rectangle formed by the points A(–1, –1), B(– 1, 4), C(5, 4) and D(5, – 1). P, Q,
   R and S are the mid-points of AB, BC, CD and DA respectively. Is the quadrilateral
   PQRS a square? a rectangle? or a rhombus? Justify your answer.

7.5 Summary

In this chapter, you have studied the following points :

1.The distance between P(x 1 , y 1 ) and Q(x 2 , y 2 ) is ()( )xx 21 ✁^22 ✂ yy 21 ✁.

2.The distance of a point P(x, y) from the origin is x^22 ✂y.

3.The coordinates of the point P(x, y) which divides the line segment joining the

points A(x 1 , y 1 ) and B(x 2 , y 2 ) internally in the ratio m 1 : m 2 are

12 21 1 2 21

12 1 2

mx m x my, m y

mm m m

✄ ✆ ✆ ☎

✞ ✟✝

✠ ✆ ✆ ✡

4.The mid-point of the line segment joining the points P(x 1 , y 1 ) and Q(x 2 , y 2 ) is

121 2,

22

☞x☛xy y☛ ✌

✍ ✎

✏ ✑

.

5.The area of the triangle formed by the points (x 1 , y 1 ), (x 2 , y 2 ) and (x 3 , y 3 ) is the

numerical value of the expression

✒ 12 3 23 1 31 2✓

(^1) ()()().
2
xy y✔ ✕x y y✔ ✕xy y✔

A NOTE TO THE READER

Section 7.3 discusses the Section Formula for the coordinates (x, y) of a

point P which divides internally the line segment joining the points

A(x 1 , y 1 ) and B(x 2 , y 2 ) in the ratio m 1 : m 2 as follows :

x =^1221

12

mx m x

mm

✖

✖

, y =^1221

12

my m y

mm

✖

✖

Note that, here, PA : PB = m 1 : m 2.

However, if P does not lie between A and B but lies on the line AB,

outside the line segment AB, and PA : PB = m 1 : m 2 , we say that P divides

externally the line segment joining the points A and B. You will study

Section Formula for such case in higher classes.