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### Course: Basic geometry and measurement>Unit 14

Lesson 2: Translations

# Translating shapes

In translations, we slide a shape around on a grid. We use the letter "T" to represent translations. We move every point of the shape a certain distance left or right, and up or down, to create a new shape that's the same size and shape as the original. We call the new shape the image.

## Want to join the conversation?

• So... The first # is the x. Then the second one is the y. And when we move those over by how many much they are we go down one too? I'm kind-of lost. (If you can't tell) Can someone please tell me how? I fell dum right now.
• erm what the flip
• never back down never what
• never give up
• You know on an office building would the windows be an example of a translation?
• Yes, as long as they are identical (same size and shape). That's a good way to look at it!
• i have no clue what im doing in math and im really confused
• You have to use the coordinates given as a guide. So for the transition (8,-1), first what you do is pick a spot where you can move it. So move point A left 8 units because it is on the x-axis and since it is a positive you move it left, if it was negative the point would be moving left.
• Graph a triangle ABC and perform a translation of (x + 4, y − 3) to create triangle A′B′C′.

Describe the transformation using words. Make sure you refer to the characteristics and the coordinates.
Draw a line through points A and A′ and through points B and B′. What do you notice about the lines you drew? Do you think you would notice the same characteristics if you drew another line through points C and C′? How do you know?
• I don't know about the graph so I can't give you a specific answer, but you need to translate triangle ABC right 4 units and down 3 units. You should notice the lines between the points are of equal distance.
• When you translate a circle, what part of the circle is translated first?
• Either the central point or the diameter.
• why is a translation called a translation?
• From https://en.wikipedia.org/wiki/Translation
The English word "translation" derives from the Latin word translatio, which comes from trans, "across" + ferre, "to carry" or "to bring" . Thus translatio is "a carrying across" or "a bringing across."
So moving a shape across a grid or from one place to another is translation.
• Bonus question: Triangle 1 is translated. If Triangle 1 has points at A = (0,0), B =(3,4), C = (3,0), and the distance from A to B' is 15, what are the coordinates of Triangle 1?
(Hints: Use the pythagorean theorem, and try graphing on desmos or geogebra)
• "How do you connect this? Oh there you go" Sal didn't you design this?
• Grown-ups with technology. We're improving to much.
• Im so confused. I'm doing IGCSE and the translation matrix has 4 numbers (0 -1). What do I do?
1 0