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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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Slope of CB × Slope of FE = 1 × (-1) = -1 [opposite and reciprocal slopes].

What is the Slope of a Line?

Slope of a line = vertical distance along the line / horizontal distance across the line = change in y / change in x.

What are Opposite and Reciprocal Slopes?

If a line has a slope of -3, the opposite and reciprocal of -3 is 1/3. Thus, if two slopes are opposite and reciprocals, when multiplied together, we would get -1.

For example, -3 × 1/3 = -1.

Find the slope of CB:

Slope of CB = change in y/change in x = (2 - 5)/(1 - 4)

Slope of CB = (-3)/(-3)

Slope of CB = 1

Find the Slope of FE:

Slope of FE = change in y/change in x = (-1 -(-4))/(2 - 5)

Slope of FE = (3)/(-3)

Slope of FE = -1

Slope of CB × Slope of FE = 1 × (-1) = -1 [opposite and reciprocal slopes].

Learn more about the slope of a line on:

https://brainly.com/question/3493733

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