Question

1. what is the mid - point of $overline{ac}$? a(2m, 2n) c(2p, 2r) e(2t, 0) (m + p, n + r) (m + n, p + r) (p - m, r - n) (m - p, n - r)

Explanation:

Step1: Recall mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Identify coordinates of A and C

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

Step3: Apply the mid - point formula

$x$ - coordinate of mid - point $=\frac{2m + 2p}{2}=m + p$.
$y$ - coordinate of mid - point $=\frac{2n+2r}{2}=n + r$.

Answer:

$(m + p,n + r)$