Question

A linear transformation is defined as L(x,y)=(-4y,2x+2y). If the input point is (−3,0), what is the image of this point under the transformation?

Answer 1

The image of the point (-3,0) under the linear transformation L(x,y) = (-4y, 2x+2y) is (0, -6).

Step-by-step explanation:

The student has asked for the image of the input point – (-3,0) under a given linear transformation L(x,y) = (-4y, 2x+2y). To find the image, we substitute the coordinates of the input point into the transformation equation.

Step 1: Substitute x = -3 and y = 0 into L(x,y).

Step 2: Calculate the new coordinates L(-3, 0) = (-4*0, 2*(-3) + 2*0) = (0, -6).

Therefore, the image of the point (-3,0) under the transformation L(x,y) is (0, -6).