Mid Point Formula (Coordinate Geometry) Grade 9th

MID
POINT
FORMULA
ISMAT RASHID

Definition:
In geometry, the midpoint is the
middle point of a line segment. It
is equidistant from both endpoints.
It bisects the line segment.

Let A(𝑥1, 𝑦1) and B(𝑥2,𝑦2) be any two points in
the plane and M(𝑥, 𝑦) be a mid point of points
A and B on the line segment AB as shown in
figure.
As 𝑃𝑄 is parallel to 𝑥 − 𝑎𝑥𝑖𝑠 and has mid point
M(𝑥, 𝑦)
Derivation of the mid point Formula

B(𝑥2,𝑦2)
A
(𝑥1, 𝑦1)
𝑀(𝑥, 𝑦)
P(𝑥1, 𝑦) Q(𝑥2, 𝑦)
O
X
X 𝑥1 𝑥2
𝑥
𝑥 − 𝑥1 𝑥2 − 𝑥
𝑥 − 𝑥1 𝑥2 − 𝑥
𝑦1
𝑦
𝑦2

So 𝑥2 − 𝑥 = 𝑥 − 𝑥1
𝑥2 + 𝑥1 = 𝑥 + 𝑥
𝑥2 + 𝑥1=2𝑥
𝑥 =
𝑥1 + 𝑥2
2
Similarly, y=
𝑦1+ 𝑦2
2
Thus the point M(𝑥, 𝑦)=M (
𝑥1+𝑥2
2
,
𝑦1+ 𝑦2
2
).

Mid-Point Formula
M(𝑥, 𝑦)=M

EXERCISE: 9.3
Qno.1
(a) A(9,2) , B(7,2)
𝑥1 𝑥2
𝑦1 𝑦2
M x, 𝑦 = M
9+7
2
,
2+2
2
M x, 𝑦 = M
16
2
,
4
2
M x, 𝑦 = M 8,2

(b) A( 2,-6),B( 3,-6)
(c) A(-8, 1),B( 6,1)
(d) A(-4, 9),B(-4,-3)
(e) A( 3,-11),B( 3,-4)
(f) A( 0, 0),B( 0,-5)
𝑥1 𝑦1 𝑥2 𝑦2
M(x,y)=M

QNo.2
Given P(𝑥1, 𝑦1)= P(-3,6) and Q(𝑥2, 𝑦2) are two points of 𝑃𝑄.
And M(5,8) is the midpoint of 𝑃𝑄.
By using Midpoint Formula: M(𝑥, 𝑦)=M(
𝑥1+𝑥2
2
,
𝑦1+𝑦2
2
)
M(5,8)=M(
−3+𝑥2
2
,
6+𝑦2
2
)
5=
−3 + 𝑥2
2
and 8=
6 + 𝑦2
2
10+3= 𝑥2 , 16-6 = 𝑦2
13= 𝑥2 , 10 = 𝑦2
Hence , Q(𝑥2, 𝑦2) = Q(13,10)

Qno.3
Given P(-2,5) , Q(1,3) and R(-1,0) are three vertices of
a right angled triangle.
Hypotenuse:
By using distance formula,
d= 𝑥2 − 𝑥1
2 + 𝑦2 − 𝑦1
2
MID POINT OF HYPOTENUSE
M x, 𝑦 = M
9+7
2
,
2+2
2
Distance of midpoint from three vertices
MP,MQ and MR

Mid Point Formula (Coordinate Geometry) Grade 9th

Mid Point Formula (Coordinate Geometry) Grade 9th

More Related Content

What's hot (20)

Similar to Mid Point Formula (Coordinate Geometry) Grade 9th (20)

Recently uploaded (20)

Mid Point Formula (Coordinate Geometry) Grade 9th