Question

What are the coordinates of vertex A of square ABCD
A(-1,-6)
B(-1,-2)
C(-1,6)
D(-2,1)​

Answer 1

The given points on the final image A''B''C''D'', and the transformation gives;

The coordinates of the vertex A of square ABCD is the option;

D. A(-2, 1)

How can the coordinate of the point A on the pre-image be found?

From the figure, we have;

A''(-5, -3), B''(-3, -1), C''(-1, -3), D''(-3, -5)

The given transformation is presented as follows;

$T_{ (- 4 , \: - 1)} \circ \:R_ {( O , \: 90^{ \circ} )}$

The formula for a rotation of 90° about the origin is presented as follows;

• (x, y) rotation of 90°→ (-y, x)

Therefore;

• (-y, x) reverse rotation of 90°→ (x, y)

Therefore;

A''(-5, -3) → A'(-5 + 4, -3 + 1) = A'(-1, -2)

B''(-3, -1) → B'(-3 + 4, -1 + 1) = B'(1, 0)

C''(-1, -3) → C'(-1 + 4, -3 + 1) = C'(3, -2)

D''(-3, -5) → D'(-3 + 4, -5 + 1) = D'(1, -4)

• A'(-1, -2) rotation of 90° reverse → A(-2, 1)

The coordinates of the vertex A of square ABCD is therefore;

D. A(-2, 1)

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Answer 2

Square A"B"C"D" has vertex A" at (-5, -3), the coordinates of vertex A before the transformation is A(-2, 1)

What is transformation?

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation.

Square A"B"C"D" has vertex A" at (-5, -3), the coordinates of vertex A before the transformation is A(-2, 1)

Find out more on transformation at: https://brainly.com/question/4289712

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