Question

What are the coordinates of the image of point (-1,5) after a counterclockwise rotation of 90* about the origin

Answer 1

In general when a point is rotated through 90° counterclockwise about the origin, first notice in which quadrant the image of the point is located. Suppose the image of point P (h, k). When you rotate it through 90° counterclockwise it takes the image M' (k, -h)
In the example M(-1,5) : it's located in the 2nd quadrant & if you  rotate it through 90° counterclockwise M' will be located in the third quadrant where both h & k are negative. So M'(-5,-1)