Find the distance between the two points rounding to the nearest tenth (if necessary). (2, 8) and (−3,−4)

13

Step-by-step explanation:

Hi there!

First, we can start by drawing the two points on a coordinate plane—just to get a sense of where they're at. We're going to solve this problem using the Pythagorean theorem by making a triangle. If you connect your two points with a line, that line will become the hypotenuse of the triangle. This is what we want to find.

The length of the base of the triangle is the distance between the x values, and the height of the triangle is the distance between the y values. We find that the x values are 5 units apart (2 - -3 = 5) and the y values are 12 units apart (8 - -4 = 12).

So: Our triangle has a base of 5 and a height of 12. We can now use Pythagorean's theorem. a^2 + b^2 = c^2, so 5^2 + 12^2 = x^2. This simplifies to 25 + 144 = x^2, or 169 = x^2.

Now we eliminate the exponent from x by taking the square root of both sides. This leaves us with x = 13.

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)