Video: Determining the Coordinates of a Point After Translation

A triangular sign with vertices shown in the given table was moved. If the new coordinates for the first two vertices are (7, 2) and (3, 2), determine the new coordinates for the third vertex.

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Video Transcript

A triangular sign with vertices shown in the given table was moved. If the new coordinates for the first two vertices are seven, two and three, two, determine the new coordinates for the third vertex.

We’re given some new coordinates. Coordinate one is now seven, two. And coordinate two is now three, two. We need to know what does that make coordinate three?

Let’s sketch a graph. We have our first original point eight, three, our second original point four, three, the third point three, 15. Here’s the original triangle sign before it’s moved. After it’s moved, the point eight, three is now located at seven, two. And the point four, three is now located at three, two.

The triangle is being moved one unit left and one unit down. And that means to find the third new point, we need to move it one unit left and one unit down. It would be located here. To move the point one unit left, we subtract one from the 𝑥-value. Three minus one is two. And to move the point down one, we subtract one from the 𝑦-coordinate. 15 minus one is 14. The new point for the third vertex is two, 14.

We connect all those points and see the new location of the triangular sign. We haven’t changed this triangle’s size or shape. We’ve simply moved it.

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