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Svetllana [295]
3 years ago
8

Based on a graph below which sequence of transformation is needed to carry ABCD onto its image A’B’C’D?

Mathematics
1 answer:
lys-0071 [83]3 years ago
4 0

Given:

The vertices of ABCD are A(2,3), B(5,6), C(8,6) and D(8,3).

The vertices of A'B'C'D' are A'(-2,6), B'(-5,3), C'(-8,3) and D'(-8,6).

To find:

The sequence of transformation is needed to carry ABCD onto its image A’B’C’D.

Solution:

The vertices of ABCD are A(2,3), B(5,6), C(8,6) and D(8,3).

If figure ABCD translated by the rule, (x,y)\to (x,y-9), then

A(2,3)\to A_1(2,-6)

B(5,6)\to B_1(5,-3)

C(8,6)\to C_1(8,-3)

D(8,3)\to D_1(8,-6)

Then the figure rotated 180 degrees clockwise about the origin. So,

(x,y)\to (-x,-y)

A_1(2,-6)\to A'(-2,6)

B_1(5,-3)\to B'(-5,3)

C_1(8,-3)\to C'(-8,3)

D_1(8,-6)\to D'(-8,6)

So, the required sequence of transformation that is needed to carry ABCD onto its image A’B’C’D is " A translation by the rule (x,y)\to (x,y-9) and then a 180° clockwise rotation about the origin".

Therefore, the correct option is D.

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