Question

Triangle LMN is similar to triangle PQR, and the hypotenuses of the triangles both lie on line X.

The slope of line X between (-7, 6) and (-4, 4) is -2/3. What is the slope of line X between (-1, 2) and (5, -2)?
A.-3/2
B.2/3
C.-2/3
D.3/2

Answer 1

C. -2/3

Explanation:

Point L is at (-7, 6), and point N is at (-4, 4). So, the slope of line X between (-7, 6) and (-4, 4) is equal to the ratio of LM to MN.

Since triangle LMN is similar to triangle PQR, the ratio of PQ to QR is equal to the ratio of LM to MN.

So, the slope of line X between points L and N is equal to the slope of line X between points P and R.

Point P is at (-1, 2), and point R is at (5, -2). Therefore, the slope of line X between (-1, 2) and (5, -2) is

Answer 2

Answer: choice C) -2/3

The line X is completely straight meaning that the slope of line X is the same no matter which two points you pick. Since we're given that line X has a slope of -2/3 through the points (-7,6) and (-4,4), this also applies to the portion from (-1,2) to (5,-2)