Question

Figure ABCD is transformed to obtain figure A'B'C'D': A coordinate grid is shown from negative 6 to 6 on both axes at increments of 1. Figure ABCD has A at ordered pair negative 4, 4, B at negative 2, 2, C at negative 2, negative 1, D at negative 4, 1. Figure A prime B prime C prime D prime has A prime at ordered pair 3, negative 4, B prime at 5, negative 2, C prime at 5, 1, D prime at 3, negative 1. Part A: Write the sequence of transformations that changes figure ABCD to figure A'B'C'D'. Explain your answer and write the coordinates of the figure obtained after each transformation. (6 points) Part B: Are the two figures congruent? Explain your answer. (4 points)

Answer 1

Given:

Vertices of ABCD are A(-4,4), (-2,2), C(-2,-1) and D(-4,1).

Vertices of A'B'C'D' are A'(3,-4), B'(5,-2), C'(5,1) and D'(3,-1).

To find:

The sequence of transformations that changes figure ABCD to figure A'B'C'D'.

Solution:

Part A:

The figure ABCD reflected across the x-axis, then

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

Using this rule, we get

$A(-4,4)\to A_1(-4,-4)$

Similarly, the other points are $B_1(-2,-2),C_1(-2,1),D_1(-4,-1)$.

Then figure translated 7 units right to get A'B'C'D'.

$(x,y)\to (x+7,y)$

$A_1(-4,-4)\to A'(-4+7,-4)=A'(3,-4)$

Similarly, the other points are $B'(5,-2), C'(5,1),D'(3,-1)$.

Therefore, the figure ABCD reflected across the x-axis and then translated 7 units right to get A'B'C'D'.

Part B:

Reflection and translation are rigid transformation, it means shape and size of figures remains same after reflection and translation.

Therefore, the two figures congruent.