Question

Triangle ABC has been rotated 90° to create triangle DEF. Using the image below, prove that lines BC and EF have the opposite and reciprocal slopes. You must show all of your work to receive credit.

Answer 1

Step-by-step explanation:

due to the 90° rotation around the point (0, 1) both lines are perpendicular (intersecting each other at 90°).

and perpendicular slopes are reciprocal with opposite signs :

a/b and -b/a

remember, the slope is the ratio

(y coordinate change / x coordinate change)

when going from one point on the line to another.

the slope of BC is B (4, 5) to C (1, 2)

x changes by -3 (from 4 to 1)

y changes by -3 (from 5 to 2)

the slope is

-3/-3 = 3/3 = 1/1 = 1

the slope of EF is E (5, -4) to (2, -1)

x changes by -3 (from 5 to 2)

y changes by +3 (from -4 to -1)

the slope is

+3/-3 = 1/-1 = -1/1 = -1

so, it matches the defined criteria for a perpendicular slope.