Question

16 unit test: reasoning about similarity and transformations - part 1
due: thu sep 11, 2025 11:59pm
attempt 1
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available: aug 18, 2025 12:00am until oct 9, 2025 11:59pm
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triangle abc is transformed to form triangle abc.
a is at (3, 1), b is at (1, 8), and c is at (7, 2).
which transformation happened to △abc to form △abc?
drag and drop the the correct answers into the each box to complete the sentence.
△abc is to form △abc

Explanation:

Step1: Analyze coordinate - changes

Original point A(3, 1), new point A' has a different position. Calculate the differences in x - and y - coordinates for all points.
For point A(3, 1) and its new position (assume we find the new coordinates from the graph precisely). Let's consider the general transformation rules.
If we look at the x - coordinates and y - coordinates of all vertices of the triangle.
For point A(3,1), if we assume the transformation rule is (x,y)→(x + a,y + b).
For point B(1,8), and for point C(7,2).
By observing the graph, we can see that the x - coordinates of all points decrease and the y - coordinates of all points decrease.
Let's take point A(3,1) and assume the new x - coordinate of A' is - 2 and new y - coordinate is - 1.
The change in x is - 2-3=-5 and change in y is - 1 - 1=-2.
We check for other points B(1,8) and C(7,2) with the same transformation rule (x,y)→(x - 5,y - 2).
For B: (1,8)→(1 - 5,8 - 2)=(-4,6)
For C: (7,2)→(7 - 5,2 - 2)=(2,0)
This shows that the transformation is a translation.

Answer:

translated 5 units left and 2 units down