Question Video: Translating a Point on the Coordinate Plane | Nagwa Question Video: Translating a Point on the Coordinate Plane | Nagwa

Question Video: Translating a Point on the Coordinate Plane Mathematics • First Year of Preparatory School

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Find the coordinates of the image of (13, 4) under the translation (𝑥, 𝑦) ⟶ (𝑥 + 5, 𝑦 − 2).

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Video Transcript

Find the coordinates of the image of the point 13, four under the translation 𝑥, 𝑦 is mapped to 𝑥 plus five, 𝑦 minus two.

We’ve been given this transformation algebraically. We can recall that the given mapping notation means that this translation has a horizontal displacement of five units and a vertical displacement of negative two units. In other words, the translation maps each point five units to the right and two units down. It’s two units down because we are subtracting two from the 𝑦-coordinate.

Applying this mapping to the point with coordinates 13, four gives the point with coordinates 13 plus five, four minus two, which is the point with coordinates 18, two. We could also apply this transformation graphically if we had access to squared paper on which to draw a coordinate grid. Here’s the point with coordinates 13, four. To add five to the 𝑥-coordinate, we move five units to the right. And then to subtract two from the 𝑦-coordinate, we move two units down. The image of the point 13, four following this translation is indeed the point with coordinates 18, two.

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