Name: Reflecting Shapes in a Line
Uploaded: 2019-07-19
Duration: 5 min 30 s
Description: This video is for you to understand the concept of reflecting shapes with examples, which will help you solve questions in exams. Watch and learn.

Question

A rhombus, $P Q R S$ , has vertices at the points $P (3, 1), Q (4, 3), R (3, 5)$ , and $S (2, 3)$ . $P Q R S$ is translated $2$ squares right and $5$ squares up. The image of $(4, 8)$ is $P' Q' R' S'$ .

Work out the coordinates of the vertices of $P' Q' R' S'$ .

Accepted Answer

We have given that a rhombus, $P Q R S$ , has vertices at the points $P (3, 1), Q (4, 3), R (3, 5)$ , and $S (2, 3)$ . $P Q R S$ is translated $2$ squares right and $5$ squares up.

We know that a translation by $(a, b)$ is a transformation that moves all points $a$ units in the x-direction and $b$ units in the y-direction.

So, to translate the rhombus $P Q R S$ $2$ , first, we move all the points $2$ squares right in the x-direction, then we move all the points $5$ squares up in the y-direction. Therefore,

The new coordinates of the point $P$ are $(5, 6)$ .

The new coordinates of the point $Q$ are $(6, 8)$ .

The new coordinates of the point $R$ are $(5, 10)$

The new coordinates of the point $S$ are $(4, 8)$

Hence, the coordinates of the vertices of $P' Q' R' S'$ are $(5, 6), (6, 8), (5, 10),$ and $(4, 8)$ .

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