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

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:

brainly.com/question/3493733

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