Question

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. if the area of δabc is 6 square units, then find a possible y-coordinate of point c. 3 4 5 6

Answer 1

(b) 4

Explanation:

You want the y-coordinate of point C on the line x=-3 so that ∆ABC has area 6 square units with segment AB being 6 units long.

Area

The formula for the area of a triangle is ...

A = 1/2bh

Given the base of 6 units, and area of 6 square units, we find the height to be ...

6 = 1/2(6)h

6/3 = h = 2

The height of the triangle is 2 units.

Coordinates

Point C is given as being on the line x=-3. Its y-coordinate must differ from the y-coordinates of A and B by 2 units. Those y-coordinates are 2, so the y-coordinate of C is ...

2 ±2 = {4, 0}

Point C may have a y-coordinate of 0 or 4. The appropriate answer choice is 4.