What is the distance between the points (7, 8) and (–8, 0) on a coordinate grid?

The distance between point and point can be found using the Pythagorean theorem.

Consider the attached image (points P and Q are meant for generic purposes and do not match the coordinates of your exercise).

You can think of PQ as the hypothenuse of the right triangle PQR, and the legnth of the legs is easy to compute, because P and R share the same y coordinate, and R and Q share the same x coordinate.

So, we have

But since and , the formula becomes

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15