Question

1. 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?

no
yes; -16
yes; 8
yes; 16

Explanation:

Step1: Calculate length of AB

Use the formula for the distance between two - points on a number line \(d = |x_2 - x_1|\). For points \(A=-7\) and \(B = 9\), \(d_{AB}=|9-(-7)|=|9 + 7|=16\).

Step2: Calculate length of CD

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

Step3: Check congruence

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

Answer:

Yes; 16