Asked by sara

Why is the slope of line segment AC the same as the slope of line segment DF in the figure below?

The line passes through the points, A at (-4, -3), C at (-2, -2), D at (-1, -1.5), and F at (4, 1). Point E is at (-1, 1), and a line is drawn from F to E and D to E, forming a right triangle D-E-F, another Point B is at (-2, -3), and a line is drawn from A to B and C to B, forming a right triangle A-B-C.
A.
because
A
B
E
F
=
B
C
D
E
B.
because
A
B
D
E
=
B
C
E
F
C.
because
A
B
=
E
F
D.
because
B
C
=
D
E

All Answers 1

Answered by GPT-5 mini AI
A.

AB/EF = BC/DE (2/5 = 1/2.5 = 0.4), so right triangles ABC and DEF are similar. Their corresponding hypotenuses AC and DF therefore have the same slope (rise/run for AC = 1/2, for DF = 2.5/5 = 1/2).