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Tcecarenko [31]
3 years ago
5

HELP PLEASE Which pair shows equivalent expressions?

Mathematics
1 answer:
pentagon [3]3 years ago
8 0

Step-by-step explanation:

3rd one is answer

i hope it helps

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Lesson 4.10 - Analytic Geometry
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Geometric shapes are mathematical shapes that include squares and triangles

<h3>How to prove the shape is a square</h3>

The side lengths of a square are congruent, and the adjacent sides are perpendicular.

So, we start by calculating the side lengths using the following distance formula

d = \sqrt{(x_1 -x_2)^2 + (y_1 -y_2)^2}

Using the above formula, we have:

AB = \sqrt{(3-2)^2 + (4+2)^2} = \sqrt{37

BC = \sqrt{(2+4)^2 + (-2+1)^2} = \sqrt{37

CD = \sqrt{(-4+3)^2 + (-1-5)^2} = \sqrt{37}

DA = \sqrt{(-3-3)^2 + (5-4)^2} = \sqrt{37}

The above shows that the side lengths of the square are congruent.

Next, calculate the slope of the sides using:

m = \frac{y_2 -y_1}{x_2 -x_1}

So, we have:

m_{AB} = \frac{4 +2}{3 -2} = 6

m_{BC} = \frac{-2 + 1}{2+4} = -\frac 16

m_{CD} = \frac{-1 -5}{-4+3} = 6

m_{DA} = \frac{5 -4}{-3-3} = -\frac 16

Notice that the opposite slopes are congruent, and the adjacent slopes are opposite reciprocal.

The above highlight, and the equal side lengths show that the figure (1) is a square

<h3>How to prove the shape is a right isosceles triangle</h3>

The legs of a right isosceles triangle are congruent, and the legs are perpendicular.

So, we start by calculating the lengths of the legs using the following distance formula

d = \sqrt{(x_1 -x_2)^2 + (y_1 -y_2)^2}

Using the above formula, we have:

XY = \sqrt{(5-4)^2 + (-1-4)^2} = \sqrt{26

XZ = \sqrt{(5-0)^2 + (-1+2)^2} = \sqrt{26

The above shows that the legs of the right isosceles triangle are congruent.

Next, calculate the slope of the legs using:

m = \frac{y_2 -y_1}{x_2 -x_1}

So, we have:

m_{XY} = \frac{5-4}{-1 -4} = -\frac{1}{5}

m_{XZ} = \frac{5-0}{-1+2} = 5

Notice that the slopes are opposite reciprocal.

The above highlight, and the equal legs show that the figure (2) is a right isosceles triangle

Read more about geometric shapes at:

brainly.com/question/14285697

7 0
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