Question

The plate is rotated 90° about the origin in the counterclockwise direction. In the rotated trapezoid, what are the coordinates of the endpoints of the side congruent to side FG?

Answer 1

You haven't provided the coordinates of the original trapezium, therefore, I can only help with the concept.

From the givens, we can know that the rotation was 90° counter-clockwise about the origin.

The rule for this rotation is:

(x , y) ..............> (-y , x)

This means that to get the points of the rotated image, negate the y-value then exchange it with the x-value

Examples:

(1 , 3) rotated 90° counter-clockwise about the origin will give (-3 , 1)

(-2 , 4) rotated 90° counter-clockwise about the origin will give (-4 , -2)

(1 , -2) rotated 90° counter-clockwise about the origin will give (2 , 1)

(-3 , -5) rotated 90° counter-clockwise about the origin will give (5 , -3)

Hope this helps :)

Answer 2

F'(-5,-7) and G'(-3,-4).

Explanation:

Consider the below figure attached with this question.

From the below figure it is clear that the vertices of trapezoid are E(-4,8), F(-7,5), G(-4,3) and H(-2,5).

If a figure is rotated 90° about the origin in the counterclockwise direction, then the rule of rotation is

`(x,y)\rightarrow (-y,x)`

We need to find the coordinates of the endpoints of the side congruent to side FG. It means we have to find F' and G'.

Using the above rule we get

`F(-7,5)\rightarrow F'(-5,-7)`

`G(-4,3)\rightarrow G'(-3,-4)`

Therefore, the endpoints of the side congruent to side FG are F'(-5,-7) and G'(-3,-4).