Question

question
what is the image of the point (-2,-7) after a rotation of 90° counterclockwise about the origin?
answer attempt 1 out of 2
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Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(90^{\circ}\) counter - clockwise about the origin, the transformation rule is \((x,y)\to(-y,x)\).

Step2: Apply the rule to the given point

For the point \((-2,-7)\), here \(x=-2\) and \(y = - 7\).
Substitute \(x\) and \(y\) into the rule:
The new \(x\) - coordinate is \(-y=-(-7) = 7\), and the new \(y\) - coordinate is \(x=-2\).

So the image of the point \((-2,-7)\) after a \(90^{\circ}\) counter - clockwise rotation about the origin is \((7,-2)\).

Answer:

$(7, - 2)$