Question

1. what is the midpoint of $overline{ec}$?

a(2m, 2n)
c(2p, 2r)
e(2t, 0)
(t + p, r)
(p, r)
(2p - 2t, r)
(p - t, 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 E and C

Given $E(2t,0)$ and $C(2p,2r)$, where $x_1 = 2t,y_1 = 0,x_2 = 2p,y_2 = 2r$.

Step3: Calculate x - coordinate of mid - point

$x=\frac{2t + 2p}{2}=t + p$.

Step4: Calculate y - coordinate of mid - point

$y=\frac{0+2r}{2}=r$.

Answer:

$(t + p,r)$