Question

find the midpoint of the joining (2,3)and (-2,1) hence show that the mid point and the end points are collinear

Answer 1

Answer:

By midpoint ,

Step-by-step explanation:

X=x1+ x2

= 2+(-2)

=0

Y= y1+y2

= 3+1

= 4

point are not collinear .....

Answer 2

The midpoint of the line joining points (2,3) and (-2,1) is (0,2).

Given,

Points A (2,3) and point B (-2,1)

To find,

The midpoint M (x,y)

Solution,

The formula to find the midpoint, M (x,y) is

x = ($x_1+x_2$)/2, y = ($y_1+y_2$)/2

⇒ x = (2 - 2) / 2

⇒ x = 0, and

y = (3+1) / 2  

⇒ y = 2

∴ The midpoint is M (0,2)

To verify that M is the midpoint of AB,

area of ΔAMC = 0

ΔAMC = 2(2-1) + 0(1-3) - 2(3-2)

⇒ ΔAMC = 2(1) - 2(1)

⇒ ΔAMC = 0

∴ This proves that the points A, M and C are collinear and the coordinates of midpoint are M (0,2).

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