Question

the coordinates of a and b are -7 and 9. the coordinates of c and d are -4 and 12. are $overline{ab}$ and $overline{cd}$ congruent? if yes, what is the length of each segment?

a) no

b) yes; -16

c) yes; 8

d) yes; 16

Explanation:

Step1: Calculate length of $\overline{AB}$

Use the distance formula for one - dimensional coordinates $d = |x_2 - x_1|$. For points $A=-7$ and $B = 9$, $d_{AB}=|9-(-7)|=|9 + 7|=16$.

Step2: Calculate length of $\overline{CD}$

For points $C=-4$ and $D = 12$, $d_{CD}=|12-(-4)|=|12 + 4|=16$.

Step3: Check congruence

Since $d_{AB}=d_{CD}=16$, $\overline{AB}$ and $\overline{CD}$ are congruent.

Answer:

D. yes, 16