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Video: Understanding the Effects of Translation on a Point

Tim Burnham

Determine the coordinates of the image of point 𝐵 of quadrilateral 𝐴𝐵𝐶𝐷 after a translation 5 units left and 3 units down.

02:03

Video Transcript

Determine the coordinates of the image of point 𝐵 of quadrilateral 𝐴𝐵𝐶𝐷 after a translation five units left and three units down.

Now a translation is a very specific sort of transformation. And basically you’re moving the shape; you’re picking it up and you’re moving it somewhere else. But importantly the shape stays exactly the same size and the same orientation. So you don’t rotate it at all; you’re just literally keeping it as it is, but moving it left and right or up and down. And also all interior angles stay the same size.

So we’re gonna be picking up this shape 𝐴𝐵𝐶𝐷 and moving it five units to the left and three units down. And we’re specifically interested in what happens to point 𝐵. Well 𝐵 starts off with an 𝑥-coordinate of negative nine and a 𝑦-coordinate of negative eight. And along with every other point on that shape, it’s gonna move five units to the left and three units down. This means that we’re gonna be subtracting five units from the 𝑥-coordinate and subtracting three units from the 𝑦-coordinate.

Now the labeling convention for a transformed point is to put a dash or a prime mark on it. So 𝐵 is gonna be transformed to point 𝐵 dashed. And the 𝑥-coordinate is gonna be negative nine take away another five, which is negative fourteen. And the 𝑦-coordinate is gonna be negative eight take away another three, so that’s negative eleven.

So the answer is that the coordinates of the image of point 𝐵, the translated point, the transformed point — let’s call it 𝐵 dashed — are gonna be negative fourteen for the 𝑥-coordinate and negative eleven for the 𝑦-coordinate.