Question

What is the image point of ( 6 , 5 ) after the transformation D 5 ∘ 0 ∘T 0,0 ​ ?

Answer 1

The image point of (6, 5) after the transformation D5 ∘ 0 ∘ T0,0 is (-30, -25).

Step-by-step explanation:

The transformation D5 ∘ 0 ∘ T0,0 is a composition of three transformations: a dilation, a translation, and a reflection. Let's break it down step by step:

1. Dilation: D5 dilates the point (6, 5) by a scale factor of 5. This means that the x-coordinate is multiplied by 5 and the y-coordinate is multiplied by 5. The image point after dilation is (30, 25).
2. Translation: The translation T0,0 leaves the point unchanged because it shifts the point 0 units in the x-direction and 0 units in the y-direction. So the image point after translation is still (30, 25).
3. Reflection: The reflection 0 reflects the point across the origin (0, 0). Since the point (30, 25) is in the first quadrant, the reflected image will be in the third quadrant. The x-coordinate is negated and the y-coordinate is negated, giving us the final image point (-30, -25) after reflection.

Therefore, the image point of (6, 5) after the transformation D5 ∘ 0 ∘ T0,0 is (-30, -25).