Question

Consider quadrilateral DEFG on the coordinate plane below. F(-5, 3) G(-2,3) E(-6, 1) D(-3,1) . After a rotation of DEFG 90° counterclockwise about the origin, which vertex will be at point (-3,-2)? E A F B D G

Answer 1

Given:

The coordinates of the vertex of the quadrilateral:

F(-5, 3) , G(-2, 3) , E(-6, 1) and D(-3, 1)

The rule for rotation 90 degrees counterclockwise about the origin is:

$(x,\text{ y) }\rightarrow\text{ (-y, x)}$

Applying this rule to the coordinates of the vertices:

$\begin{gathered} F(-5,\text{ 3) }\rightarrow\text{ F'(-3, -5)} \\ G(-2,\text{ 3) }\rightarrow\text{ G'(-3, -2)} \\ E(-6,\text{ 1) }\rightarrow\text{ E'(-1, -6)} \\ D(-3,\text{ 1) }\rightarrow\text{ D'(-1, -3)} \end{gathered}$

Hence, the vertex at the point (-3, -2) is the point G