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.

Lines BC and EF have the opposite and reciprocal slopes given that triangle ABC has been rotated 90° to create triangle DEF. This can be obtained by finding the slopes of each line and comparing them.

Prove that lines BC and EF have the opposite and reciprocal slopes:

Slope of a line can be obtained using the equation,

m = rise/run = Δy/Δx = (y₂ - y₁)/(x₂ -x₁)

where m is the slope of the triangle, (x₁, y₁) and (x₂, y₂) are the endpoints of the lines. (y₂ - y₁) is the rise and (x₂ -x₁) is the run.

Slope of a line can also be found using the formula,

m = rise/run = Δy/Δx = tan(∅)

where ∅ is the angle between Δx(run) and hypotenuse

From the question we can calculate the slope using the formula of slope,

In triangle ABC,

(4, 5) and (1, 2) are the endpoints of the line BC

Slope of the line BC,

m₁ = (y₂ - y₁)/(x₂ -x₁) = (2 - 5)/(1 - 4)

m₁ = -3/-3

m₁ = 1

In triangle DEF,

(2, -1) and (5, -4) are the endpoints of the line EF

Slope of the line EF,

m₂ = (y₂ - y₁)/(x₂ -x₁) = (-4 - (-1))/(5 - 2)

m₂ = -3/3

m₂ = - 1

Slope of the line BC is 1 and slope of line EF is - 1, and 1 and - 1 are opposite and reciprocal.

Since lines BC and EF have the opposite and reciprocal slopes given that triangle ABC has been rotated 90° to create triangle DEF.

Learn more about slopes here:

brainly.com/question/17870676

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