Answer:
The length of A'C' will also be 5 units.
Step-by-step explanation:
If a reflection takes triangle CAT to C'A'T', what is A'C'?
Starting with ΔCAT triangle as shown in figure (a).
Reflections are said to be Isometries as it does preserve the distances.
If the shape or triangle ΔCAT reflected it will remain the same size. As a result, the reflected image would be 'congruent' to the original object.
Lets suppose, ΔCAT is reflected across y axis.
The rule for reflection of the point (x,y) across the y-axis is actually the point (-x,y).
Reflect a point across the y-axis, the y-coordinate will remain the same, but the x-coordinate will be transformed into its opposite (the sign of x-coordinate will be changed).
C(0, 0) → C'(0, 0)
A(-2, 1) → A'(2, 1)
T(-1, 4) → T(1, 4)
length of Side AT = 3 units
length of Side TC = 4 units
length of Side AC = 5 units
As reflections are said to be Isometries as it does preserve the distances.
So, if ΔCAT reflected is reflected across y axis. ΔC'A'T' preserves the distances. The length of each segment of the preimage would be equal to its corresponding side in the image as shown in figure (a).
So, the length of A'C' will also be 5 units.
Keywords: reflection, transformation, triangle
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Answer:
The length of A'C' will also be 5 units.
Step-by-step explanation:
