Question

What is the midpoint of AC?

Answer 1

Answer:

$(m+p,n+r)$

Step-by-step explanation:

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

The midpoint is calculated using the formula;

$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Substitute the coordinates to get;

$M=(\frac{2m+2p}{2},\frac{2n+2r}{2})$

$M=(\frac{2(m+p)}{2},\frac{2(n+r)}{2})$

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

Answer 2

Answer:

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

Step-by-step 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)]