Question

What is the midpoint of AC?

Answer 1

The coordinates of midpoint of AC = [ (m + p), (n + r)]

Explanation:

The midpoint of the line joining the the coordinates(x₁,y₁) and (x₂,y₂) is given by,

(x,y) = [(x₁ + x2)/2 , (y₁ + y₂)/2]

To find the midpoint of AC

It is given that,

A(2m, 2n) and C(2p, 2r)

Here, (x₁,y₁) = (2m, 2n)

(x₂,y₂) = (2p, 2r)

The midpoint of AC, (x, y) = [(x₁ + x2)/2 , (y₁ + y₂)/2]

= [(2m + 2p)/2 , (2n + 2r)/2]

=[ (m + p), (n + r)]

Therefore the coordinates of midpoint of AC = [ (m + p), (n + r)]

Answer 2

`(m+p,n+r)`

Explanation:

Let
`(x_1,y_1)=A(2m,2n)` and
`(x_2,y_2)=C(2p,2r)`.

The midpoint is calculated using the formula;

`M=((x_1+x_2)/(2),(y_1+y_2)/(2))`

Substitute the coordinates to get;

`M=((2m+2p)/(2),(2n+2r)/(2))`

`M=((2(m+p))/(2),(2(n+r))/(2))`

`M=(m+p,n+r)`