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Andrews [41]
3 years ago
15

What is the perimeter of ^PQR with vertices P(-2,9) Q(7,-3) and R(-2,-3) in the coordinate plane?

Mathematics
1 answer:
e-lub [12.9K]3 years ago
5 0
Using the distance formula we can determine the perimeter of PQR.

Distance formula: d=√(x-x1)^2+(y-y1)^2
distance of PR: √(-2+2)^2+(9+3)^2= 12
distance of QR: √(7+2)^2+(-3+3)^2=9
distance of PQ: √(7+2)^2+(-3-9)^2= 15

Perimeter: 12+9+15=36
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<u>We will proceed to find the equations in the vertex form in each case</u>

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Group terms that contain the same variable, and move the constant to the opposite side of the equation

y-38= 4x^{2}+24x

Factor the leading coefficient

y-38= 4(x^{2}+6x)

Complete the square. Remember to balance the equation by adding the same constants to each side

y-38+36= 4(x^{2}+6x+9)

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y= 4(x+3)^{2}+2

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Group terms that contain the same variable, and move the constant to the opposite side of the equation

y-38= 4x^{2}-24x

Factor the leading coefficient

y-38= 4(x^{2}-6x)

Complete the square. Remember to balance the equation by adding the same constants to each side

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Group terms that contain the same variable, and move the constant to the opposite side of the equation

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y+7= 4(x+1.5)^{2}

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Group terms that contain the same variable, and move the constant to the opposite side of the equation

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y+3= 4(x+2)^{2}

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<u>the vertex is the point (-2,-3)</u>

therefore

<u>the answer is </u>

y= 4x^{2}+24x+38

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