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.

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Tanvigupta426id Tanvigupta426id · Answer 1

BC and EF have the opposite and reciprocal slopes.

According to the statement

we have given that the

Triangle ABC has been rotated 90° to create triangle DEF.

And we have to find the lines BC and EF have the opposite and reciprocal slopes.

So, For this purpose,

We know that the

Slope of a triangle represents the angle that are formed between positve X-axis moving anticlockwise towards y-axis.

And From triangle ABC

The slope of triangle ABC

AB = 4 and AC = 4 Then

slope of triangle = perpendicular / base

slope of triangle ABC = 4/4

so, it become tan45 degree which is 1.

So, Slope of BC is 1.

slope of triangle DEF = 4/-4

so, it become tan135 degree which is -1.

So, Slope of EF is -1.

Slope of ABC is 1, where as

Slope of DEF is -1

∴ BC and EF have the opposite and reciprocal slopes.

Learn more about the slopes here

https://brainly.com/question/3493733

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