Video: Naming Coordinates of Vertices of Isosceles Triangles

Give the coordinates of the vertices 𝐴 and 𝐢.


Video Transcript

Give the coordinates of the vertices 𝐴 and 𝐢.

Before we give the coordinates of 𝐴 and 𝐢, 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 𝐡 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 𝐢, we need to find their π‘₯- and 𝑦-coordinates. 𝐴 is located 𝐴 units along the π‘₯-axis and 𝐴 units along the 𝑦-axis. The 𝐢 vertex is located at zero units left or right, zero units on the π‘₯-axis and 𝐴 units on the 𝑦-axis, 𝐴 units up. The two missing vertices can be labeled as 𝐴 π‘Ž, π‘Ž, and 𝐢 zero, π‘Ž.

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