Question

Use the image to answer the question.

An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 8 to 8 in increments of 1. A triangle A B C is plotted on the graph. The triangle A B C has its vertices marked with closed points at A left parenthesis 2 comma 4 right parenthesis, B left parenthesis 6 comma 6 right parenthesis, and C left parenthesis 6 comma 2 right parenthesis.

Given point A (2, 4)
on the triangle in Quadrant I, where is the new point if the triangle is rotated 90 degrees counterclockwise?

(1 point)
Responses

(4,−2)
left parenthesis 4 comma negative 2 right parenthesis

(−4, 2)
left parenthesis negative 4 comma 2 right parenthesis

(−4,−2)
left parenthesis negative 4 comma negative 2 right parenthesis

(−2,−4)
left parenthesis negative 2 comma negative 4 right parenthesis
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Answer 1

To find the new coordinates of point A (2, 4) after a 90-degree counterclockwise rotation around the origin, we can use the following transformation:

When a point (x, y) is rotated 90 degrees counterclockwise, its new coordinates become (-y, x).

Applying this to point A:

1. Original coordinates: A (2, 4)
2. After rotation: A' (-4, 2)

So the new coordinates of point A after rotating the triangle 90 degrees counterclockwise are (-4, 2).

The correct response is: **(−4, 2)**.