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Identify and Perform Translations

Students describe a translation using a vector (horizontal shift, vertical shift) and perform translations on figures on the coordinate plane. They verify that translations preserve line lengths, angle measures, and parallelism, producing congruent images.

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Identify and Perform Translations

Grade 8 · Geometry: Transformations · question 1 of 3

0 of 20

20 rungs. A star at the top.

U−8−6−4−22468−8−6−4−224680

Once point U is translated 1 right and 2 down, report the x-coordinate of U′.

Perform the move.

How it is taught

0:00 of 4:03

A translation slides every point the same way.

There is no turning and no flipping.

BCDEB′C′D′E′−8−6−4−22468−8−6−424680

Read it: Translations on the coordinate plane

Triangle PQR slides 5 right and 4 down. Every point moves the same way, so every point follows (x, y) → (x + 5, y − 4). R(−1, 3) lands at R′(4, −1).

  1. Read the slide: right or left changes x, up or down changes y.
  2. Write it as a rule: right or up adds, left or down takes away.
  3. Apply the rule to each vertex, then join the images in the same order.

A translation moves every point the same distance in the same direction.

Nothing turns or stretches, so the image keeps every side length and every angle.

For R(−1, 3): −1 + 5 = 4 and 3 − 4 = −1, so R′ is at (4, −1).

A translation adds the same amount to every x and the same amount to every y.

Sliding the wrong way: adding 4 to y when the slide is 4 down.

Down and left take away; up and right add. 4 down is y − 4, so 3 becomes −1.

Point P(−9, 3) is translated 3 right and 2 down. What is the x-coordinate of P′? — −6. Right adds 3 on x: −9 + 3 = −6.

Translate △ABC by ⟨7, −3⟩

A translation slides every point of a shape the same distance in the same direction — no turning, no flipping.

Here's the coordinate plane with triangle ABC drawn on it.

The vertices are A at negative five, two; B at negative three, four; and C at negative two, one.

Grade 8 · Sliding a triangle on the coordinate plane

We'll translate using the vector seven, negative three — that means right seven, down three.

Start with A. Slide right seven and down three to land at A prime, two and negative one.

Now B slides the same way — right seven, down three — to B prime at four, one.

And C slides to C prime at five, negative two.

Connect A prime, B prime, and C prime to draw the image triangle.

Notice the side lengths and angles are exactly the same. Translations always produce congruent images.

The rule is x comma y goes to x plus seven, y minus three. Same triangle, just moved.

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

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.

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