Question

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. (1 point)

5
6
7
8

Answer 1

7

Explanation:

A = 1/2 (b)(h)

12.5 = 1/2 (5)(h)

Multiply both sides by 1/2 or 2 to cancel out the fraction

2 x 12.5 = 1/2 (5)(h) x 2

25 = 5h

Divide both sides by 5 to get h on its own

25/5 = 5h/5

h = 5

HOWEVER, 5 is not our answer because we started on y = 2.

So,

5 + 2 = 7

Answer 2

Answer: The area of right triangle ABC can be found using the formula (1/2)bh, where b is the length of the base and h is the height. Since the base of the triangle is 5 units and the area is 12.5 square units, the height must be 2.5 units.

Knowing that point C is on the line x = -2, we can use the height of 2.5 units to find the y-coordinate of point C.

Starting from the line y = 2, moving 2.5 units down will give us a y-coordinate of y = 2 - 2.5 = -0.5.

So, a possible y-coordinate of point C is -0.5.

Explanation: