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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.

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 a class=

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reinhard10158

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.

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