Question

value: 1
is point z the mid - point of $overline{xy}$?
$x(-2.4,3)$
$z(1.4,2.7)$
$y(4.2,2.6)$

a. yes. the mid - point of $overline{xy}$ is $(1.4,2.7)$
b. no. the mid - point of $overline{xy}$ is $(1.2,2.8)$

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1=-2.4,y_1 = 3,x_2 = 4.2,y_2=2.6$.

Step2: Calculate x - coordinate of mid - point

$x=\frac{-2.4 + 4.2}{2}=\frac{1.8}{2}=0.9$.

Step3: Calculate y - coordinate of mid - point

$y=\frac{3+2.6}{2}=\frac{5.6}{2}=2.8$.
So the mid - point of $\overline{XY}$ is $(0.9,2.8)$.

Answer:

B. No. The midpoint of $\overline{XY}$ is $(1.2,2.8)$ (Note: There is a calculation error in option B, the correct mid - point is $(0.9,2.8)$ but among the given options, the answer based on the process of elimination is B as the mid - point is not $(1.4,2.7)$)