Maths

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 ( x
2
x ) ( y
2
y ) .
2 1 2 1
2
2. The distance of a point P(x, y) from the origin is x y
2 . ✂
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
mx
1 2
m2x1,
my
1 2
m ✄
2
☎ y
✆
1 ✆
✞ ✟✝
✆
✆
✠
✡
m m m m
1 2 1 2
4. The mid-point of the line segment joining the points P(x 1
, y 1
) and Q(x 2
, y 2
) is
.
☛ ☛
☞
✌
✍
✎
✏ ✑
✒
✓
x1 x2 ,
y1 y2
2 2
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
1
1( 2
2 x y y 3) x 2( 3 y 1) x 3( 1 y 2) .
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 =
mx
m
mx ✖
m
1 2 2 1
1 2
✖
, y =
my
m
my ✖
m
1 2 2 1
1 2
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.
✖