Question

quadrilateral efgh has coordinates e(a, a), f(3a, a), g(2a, 0), and h(0, 0). find the mid - point of $overline{ef}$.
(a, 2a)
(2a, 0)
(2a, a)
(a, a)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for 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 F

For points $E(a,a)$ and $F(3a,a)$, $x_1=a,y_1=a,x_2 = 3a,y_2=a$.

Step3: Calculate x - coordinate of mid - point

$x=\frac{a + 3a}{2}=\frac{4a}{2}=2a$.

Step4: Calculate y - coordinate of mid - point

$y=\frac{a + a}{2}=\frac{2a}{2}=a$.

Answer:

$(2a,a)$