Skip to content
Brainsladder

Describe Transformations Using Coordinates

Students apply translations, rotations, reflections, and dilations to figures given as coordinate vertices and describe the effect of each transformation on the coordinates. They determine the rule for a transformation from a pre-image and its image.

Try three of them

Real questions from this skill, graded here. No account, and nothing is saved.

Describe Transformations Using Coordinates

Grade 8 · Geometry: Transformations · question 1 of 3

0 of 20

20 rungs. A star at the top.

S−8−6−4−22468−8−6−4−224680

Given point S is rotated 180 degrees about the origin, type S′'s x-coordinate.

Perform the move.

How it is taught

0:00 of 4:20

A transformation moves every vertex by a rule.

The new coordinates of each point are the image.

S−8−6−4−22468−8−6−4−224680

Read it: Describing a move with coordinates

Segment MN slides to M′N′. M(−3, 4) goes to M′(−1, −1): x changes by −1 − (−3) = 2 and y by −1 − 4 = −5. The rule is (x, y) → (x + 2, y − 5).

  1. Pick one vertex and its image.
  2. Take each original coordinate from the image's: that is the change in x and in y.
  3. Write the rule and check it on a second vertex.

Every point of a slide moves by the same amount, so one vertex gives the rule for all of them.

N(1, 4) follows the same rule: 1 + 2 = 3 and 4 − 5 = −1, so N′ is (3, −1).

A rule like (x, y) → (−x, y) is a flip, and (x, y) → (−y, x) is a turn.

The change is the image's coordinate minus the original's.

Subtracting the wrong way round: −3 − (−1) = −2, which reverses the move.

Always image minus original: −1 − (−3) = 2, so the slide is 2 right.

The rule (x, y) → (x + 6, y + 1) moves the point (3, 6). What is the y-coordinate of its image? — 7. The rule adds 1 to y: 6 + 1 = 7.

Translate △ABC by (x+3, y−1)

When we transform a shape, the coordinates of every vertex change in a predictable way. Let's see how.

Here's our coordinate grid, with the x-axis going right and the y-axis going up.

Triangle ABC has vertex A at one comma two, B at three comma two, and C at two comma four.

Grade 8 · Sliding a triangle on the coordinate plane

We'll translate the triangle using this rule: x becomes x plus three, and y becomes y minus one.

Start with A. One plus three is four. Two minus one is one. So A prime lands at four comma one.

Now B. Three plus three is six. Two minus one is one. B prime is at six comma one.

Finally C. Two plus three is five. Four minus one is three. C prime is at five comma three.

Connect the new vertices. Triangle A prime B prime C prime is our image.

Notice the image is the same shape and size — it just slid three units right and one unit down.

A translation by (x plus three, y minus one) shifts every point three right and one down. That's the power of coordinates!

Now you try. Find the x-coordinate of A prime. What is x of A'?

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

More of the library

Every skill has a page

Practise this skill free

14 days of every skill, practice packets, Fluency sheets and up to four students. No card.

Start free