Best answer gets

right triangle abc is on a coordinate plane. segment ab is on the line y = 2 and is 6 units long. point c is on the line x = −3. what is the y-value of point c if the area of δabc is 9 units squared?

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Explanation:

The line y = 2 is a horizontal line passing through 2 on the y axis. Every point on this line has a y coordinate of 2. Since both A and B are on this line, this means AB is horizontal as well. This can be thought of as the base of the triangle. AB = 6 is the length of the base.

We don't know the height, so we'll call that h.

We do know the triangle area is 9 square units

The formula we'll use is

area = (base*height)/2

Plug in the given values and solve for h

9 = (6*h)/2

9*2 = 6h

18 = 6h

6h = 18

h = 18/6

h = 3

The height of the triangle is 3. This means that point C is either 3 units below y = 2 or point C is 3 units above y = 2.

If points C is 3 units below y = 2, then its y coordinate would be 2-3 = -1. But this isn't an answer choice. So we ignore this scenario.

If point C is 3 units above y = 2, then this point has a y coordinate of 2+3 = 5.

Below is one possible diagram of how the triangle could look like. Point C is always fixed at (-3,5); however point A is allowed to slide around as long as it has a y coordinate of y = 2. Point B is a similar story as point A. Furthermore, segment AB must always be 6 units long.

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