Question

What is the perimeter of parallelogram $A B C D$ that has vertices with $(x, y)$ coordinates $A(-3,-2), B(-1,5), C(4,6),$ and $D(2,-1) ?$ F. 15 G. $2 \sqrt{10}+2 \sqrt{29}$ H. $2 \sqrt{53}+2 \sqrt{26}$ J. $2 \sqrt{79}$ K. 158

Name: Problem 50, Chapter :
Uploaded: 2020-08-20T21:18:33-08:00
Duration: 3 min 37 s
Channel: James Kiss
Description: What is the perimeter of parallelogram A B C D that has vertices with (x, y) coordinates A(-3,-2), B(-1,5), C(4,6), and D(2,-1) ? F. 15 G. 2 √(10)+2 √(29) H. 2 √(53)+2 √(26) J. 2 √(79) K. 158

   What is the perimeter of parallelogram $A B C D$ that has vertices with $(x, y)$ coordinates $A(-3,-2), B(-1,5), C(4,6),$ and $D(2,-1) ?$
F. 15
G. $2 \sqrt{10}+2 \sqrt{29}$
H. $2 \sqrt{53}+2 \sqrt{26}$
J. $2 \sqrt{79}$
K. 158

Instant Answer

Solved by Expert James Kiss

08/20/2020

Step 1

We can find the length of each side using the distance formula, which is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. Show more…

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What is the perimeter of parallelogram $A B C D$ that has vertices with $(x, y)$ coordinates $A(-3,-2), B(-1,5), C(4,6),$ and $D(2,-1) ?$ F. 15 G. $2 \sqrt{10}+2 \sqrt{29}$ H. $2 \sqrt{53}+2 \sqrt{26}$ J. $2 \sqrt{79}$ K. 158

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Key Concepts

Properties of a Parallelogram

A parallelogram is a quadrilateral in which opposite sides are both equal in length and parallel. These properties allow one to calculate the perimeter by finding the lengths of two adjacent sides and then doubling their sum, as the other two sides will mirror these lengths.

Perimeter Calculation

The perimeter of any polygon, including a parallelogram, is the total distance around the shape. This is computed by summing the lengths of all its sides. In the case of a parallelogram, by using the properties of equal opposite sides, the calculation simplifies to twice the sum of the lengths of any two adjacent sides.

Distance Formula

The distance formula is used to calculate the length between any two points in the coordinate plane. It is derived from the Pythagorean theorem and is crucial for determining side lengths when the coordinates of the endpoints are known.

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