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Question Video: Naming Coordinates of Vertices of Isosceles Triangles Mathematics • 11th Grade

Give the coordinates of the vertices ๐ด, ๐ต, and ๐ถ.


Video Transcript

Give the coordinates of vertices ๐ด, ๐ต, and ๐ถ.

What can we notice about this triangle? We notice that sides ๐ด๐ต and sides ๐ด๐ถ are equal in length. We also know because of the intersection of the ๐‘ฅ- and ๐‘ฆ-axis that we have a right angle. Points ๐ถ and ๐ต are located along the ๐‘ฅ-axis. Because they intersect the ๐‘ฅ-axis, it tells us something about the height. Point ๐ถ is negative ๐‘Ž units to the left and zero units up. We donโ€™t know how many units to the right point ๐ต is. We donโ€™t know its ๐‘ฅ-coordinate. But we do know that it is located zero units up on the ๐‘ฅ-axis. So we have an unknown for the ๐‘ฅ-value but zero for the ๐‘ฆ-value.

Something else we can say about this triangle is that the height provides a perpendicular bisector. And that means that it cuts side ๐ต๐ถ in half. The distance from zero to the origin is the same distance as ๐ต to the origin. ๐ถ is located ๐‘Ž distance from the origin. And that means ๐ต will also be located ๐‘Ž units away from the origin. ๐ต would be located at ๐‘Ž, zero.

Our final missing value is the ๐‘ฅ-coordinate of our point ๐ด. The ๐‘ฅ-coordinate tells us how far left or right that point is. Point ๐ด is located on the ๐‘ฆ-axis. It is not to the left or to the right of the ๐‘ฆ-axis. The ๐‘ฆ-intercepts always have zero as their ๐‘ฅ-coordinate. ๐ด would be located at zero, ๐‘.

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