Question

GR has coordinates G (2,-2) and R (3,8) and H is the result of the dilation centered at the origin, and it is the result of HM centered at the origin. The coordinates of HM (-1,1) and M (-1.5,-4). Complete the following algebraic description that represents the transformation of HM.

Answer 1

To determine the transformation of vector HM, compare the coordinates of H and HM to find the scale factor 'k'. Multiply both x and y coordinates of HM by 'k' to find the transformed coordinates of H.

Step-by-step explanation:

The student has asked about the transformation of a vector HM via dilation from the origin and wants to find the algebraic description of this transformation. The coordinates for points G, R, H, M, and HM are given, and part of the question involves understanding how displacement vectors and their transformations work, specifically through analytic methods and geometric constructions.

Step-by-Step Explanation:

To find the algebraic description of the transformation that maps HM to H:

1. Look at the coordinates of HM and H.
2. Determine the scale factor of dilation by comparing the coordinates of H with those of HM.
3. Apply the scale factor to both the x and y coordinates to obtain the transformed coordinates.

For example, if HM has coordinates (-1,1) and H has coordinates after a transformation that we are trying to determine, we can see that if the x-coordinate is multiplied by a scale factor 'k', then

k * (-1) = Hx

and

k * 1 = Hy

Using these equations, we can find the value of 'k' that is the scale factor for the dilation centered at the origin.