Question Video: Translating a Shape on a Grid | Nagwa Question Video: Translating a Shape on a Grid | Nagwa

# Question Video: Translating a Shape on a Grid Mathematics • First Year of Preparatory School

## Join Nagwa Classes

Attend live Mathematics sessions on Nagwa Classes to learn more about this topic from an expert teacher!

In the figure below, determine the coordinates of the points π΄β²π΅β²πΆβ²π·β², where π΄β²π΅β²πΆβ²π·β² is a translation of π΄π΅πΆπ· by (β2, β5).

03:17

### Video Transcript

In the figure below, determine the coordinates of the points π΄ prime, π΅ prime, πΆ prime, and π· prime, where π΄ prime π΅ prime πΆ prime π· prime is a translation of π΄π΅πΆπ· by negative two, negative five.

A translation is a transformation which moves a shape up or down and from side to side. A translation of negative two, negative five means the shape moves two places to the left and five places down. Seen as weβre translating a shape with four points, we have four coordinates to translate. There are a couple of ways we can find the images of each point after the translation. But letβs start by doing this graphically.

Weβll start with point π΄. If we move the point π΄ two units to the left and five units down, we find that the image of π΄, π΄ prime, is at the point six, one. Letβs do the same with point π΅. We move point π΅ two units to the left and five units down. And we find that the image of π΅, π΅ prime, is at the point six, negative four. Now letβs translate the point πΆ. We move the point πΆ two units to the left and five units down. And we find that the image of πΆ, πΆ prime, is at the point negative one, negative four. Finally, letβs translate the point π·. We move the point π· two units to the left and five units down. And we find that the image of π·, π· prime, is at the point one, negative one. Then, joining all our points, we see the translated shape π΄ prime π΅ prime πΆ prime π· prime.

Now we can read the coordinates of the translated points directly from the graph to get our answer. But letβs also see a different method we could have used. For a translation with horizontal displacement of π units and a vertical displacement of π units, the point π₯, π¦ maps to π₯ add π, π¦ add π. Here are the coordinates of the four points we were given in the question: π΄, π΅, πΆ, and π·. We can use the formula above to map each point to its image. The horizontal displacement is negative two, so π is negative two. The vertical displacement is negative five, so π is negative five.

So we calculate the image of each of these coordinates by adding negative two to the π₯-coordinate and negative five to the π¦-coordinate, which then allows us to calculate the images of each of these points. That is, π΄ prime is six, one; π΅ prime is six, negative four; πΆ prime is negative one, negative four; and π· prime is one, negative one. Then, we can check these points by looking at the translation we carried out on the graph. And we see that the points match up.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions