Video: Naming Coordinates of Vertices of Isosceles Triangles

Video Transcript

Give the coordinates of the vertices 𝐴 and 𝐶.

Before we give the coordinates of 𝐴 and 𝐶, we need to identify what we know about this figure. Two sides, two adjacent sides, of this figure have equal lengths. In addition to that, there’s a right angle inside this figure. Because there’s a right angle in this closed four-sided figure, we know that all of the angles inside this figure are right angles.

And these two pieces of information confirm for us that this figure would be a square. Therefore, all four sides of this figure are equal. One of the coordinates is at the origin at zero, zero. And coordinate 𝐵 is at 𝐴. And that means it goes from zero to 𝐴. The length of this side is 𝐴 units, which makes the length of all of the sides 𝐴 units.

To label the vertices 𝐴 and 𝐶, we need to find their 𝑥- and 𝑦-coordinates. 𝐴 is located 𝐴 units along the 𝑥-axis and 𝐴 units along the 𝑦-axis. The 𝐶 vertex is located at zero units left or right, zero units on the 𝑥-axis and 𝐴 units on the 𝑦-axis, 𝐴 units up. The two missing vertices can be labeled as 𝐴 𝑎, 𝑎, and 𝐶 zero, 𝑎.