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

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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