Right triangle ABC is on a coordinate plane. Segment AB is on the line y = 2 and is 5 units long. Point C is on the line x = −2. If the area of ΔABC is 12.5 square units, then find a possible y-coordinate of point C. 5 6 7 8

Step-by-step explanation:

Segment AB is on the line y = 2 which is a horizontal line. Point C is on the line x = -2, which is a vertical line. These 2 lines will cross each other and form a right angle...the right angle in the right triangle in question. The formula for the area of a triangle is

The segment AB, being a horizontal line, is the base of our triangle and point C is somewhere on the height. If we can find the height of the triangle, we can add or subtract that height from y = 2 to get the possible y coordinate of point C. We already know the x coordinate (it's -2).

and

25 = 5h so

h = 5. That means that we can either add 5 to the y coordinate of 2, or we can subtract 5 from the y coordinate of 2 to get the possible y coordinate of point C.

2 + 5 = 7 so the coordinate for C could be (-2, 7) or

2 - 5 = -3 so the coordinate for C could also be (-2, -3).

Since -3 is not in our choices but 7 is, the one you want is 7.