Right triangle ABC is on a coordinate plane. Segment AB is on the line y = 2 and is 3 units long. Point C is on the line x = −1. If the area of ΔABC is 12.5 square units, then find a possible y-coordinate of point C.

and

Step-by-step explanation:

Segment AB is on the line y = 2 and is 3 units long. Consider this segment as the base of the triangle ABC.

Use the formula

for the area of the triangle. Then

There are two possible points C which lie on the line x = -1 and are at the distance of units from the line y = 2.

Point has y-coordinate

Point has y-coordinate

31/3

Step-by-step explanation:

Given that Segment AB is on the line y = 2, then y-coordinate is 2 for points A and B.

Given that Point C is on the line x = −1, then one point A or B must has -1 as x-coordinate. Let's assume that A is point (-1, 2). Given that Segment AB is 3 units long, then B must be at (2, 2) (the x-coordinate is -1 + 3 = 2).

The x-coordinate of C is -1.

Right triangle ABC  are formula:

Area = (AB * AC)/2

12.5 = (3 * AC)/2

12.5*2/3 = AC

25/3 = AC

That is, segment AC is 25/3 units long. Both A and C have the same x-coordinate, then:

yC - yA = 25/3

where  yC and yA are the y-coordinates of C and A. So:

yC - 2 = 25/3

yC = 25/3 + 2

yC = 31/3