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# Coordinates

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The points (1,-2) and (4,-10) are adjacent vertices of a square. What is the perimeter of the square?

Dec 19, 2021

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To find the perimeter, we must first find the distance from (1, -2) to  (4, -10). To do this, we can use the distance formula.

$$\sqrt((x\delta)^2+(y\delta)^2),$$ where $$\delta$$=the change in positioning for the point.

We can plug in for this equation to get $$\sqrt((4-1)^2+(-10--2)^2)$$

Simplifying this, we get $$\sqrt(3^2+(-8)^2)$$, then $$\sqrt(9+64)$$, and finally $$\sqrt73$$

Since there are 4 sides to a square, multiply $$\sqrt73$$ by 4 to account for all sides.

The final answer should be $$4\sqrt73$$ since 73 is prime.

Dec 19, 2021