Give the coordinates of vertices 𝐴, 𝐵, and 𝐶.
What can we notice about this triangle? We notice that sides 𝐴𝐵 and sides 𝐴𝐶 are equal in length. We also know because of the intersection of the 𝑥- and 𝑦-axis that we have a right angle. Points 𝐶 and 𝐵 are located along the 𝑥-axis. Because they intersect the 𝑥-axis, it tells us something about the height. Point 𝐶 is negative 𝑎 units to the left and zero units up. We don’t know how many units to the right point 𝐵 is. We don’t know its 𝑥-coordinate. But we do know that it is located zero units up on the 𝑥-axis. So we have an unknown for the 𝑥-value but zero for the 𝑦-value.
Something else we can say about this triangle is that the height provides a perpendicular bisector. And that means that it cuts side 𝐵𝐶 in half. The distance from zero to the origin is the same distance as 𝐵 to the origin. 𝐶 is located 𝑎 distance from the origin. And that means 𝐵 will also be located 𝑎 units away from the origin. 𝐵 would be located at 𝑎, zero.
Our final missing value is the 𝑥-coordinate of our point 𝐴. The 𝑥-coordinate tells us how far left or right that point is. Point 𝐴 is located on the 𝑦-axis. It is not to the left or to the right of the 𝑦-axis. The 𝑦-intercepts always have zero as their 𝑥-coordinate. 𝐴 would be located at zero, 𝑏.