Question

the base of right triangle abc is shown on the coordinate plane, with vertex a and vertex b marked.
the height of the triangle is 4 units. the length of side ac is 4 units.
at what point is vertex c located?

Explanation:

Step1: Identify coordinates of A

The coordinates of point A are (3, 2) as seen from the graph.

Step2: Recall height property

Since the height of the right - triangle is 4 units and side AC is 4 units, and the triangle is right - angled, and the base is horizontal (AB is horizontal), to find point C, we move 4 units up from point A along the vertical line passing through A.

Step3: Calculate coordinates of C

The x - coordinate of C will be the same as that of A (x = 3), and the y - coordinate of C will be \(y=2 + 4=6\). So the coordinates of C are (3, 6).

Answer:

(3, 6)