1. A rectangular prism is defined as the drawing shows. Note B at (0, 5, 0) and F (0, 0, 4). The prism is reflected over the xz-
plane. The reflected image is then translated 2 units back, 3 units left, and 1 unit up. a.) Show the results of your calculations for points A, B, C and D from the reflection.
b.) Show the results of your calculations for points A, B, C and D from the translation.
Initial coordinates: A (0,0,0) B (0,5,0) C (3,5,0) D (3,0,0) E (3,0,4) F (0,0,4) G (0,5,4) H (3,5,4)
<span>a.) The prism is reflected over the xz-plane. Reflection Point P(x,y,z) over the xz-plane is P'(x,-y,z): Reflection P(x,y,z) over the xz-plane → P'(x,-y,z)
Reflection A(0,0,0) over the xz-plane → A'(0,-0,0) = A'(0,0,0) </span>Reflection B(0,5,0) over the xz-plane → B'(0,-5,0) Reflection C(3,5,0) over the xz-plane → C'(3,-5,0) Reflection D(3,0,0) over the xz-plane → D'(3,-0,0) = D'(3,0,0)
b.) <span>The reflected image is then translated 2 units back, 3 units left, and 1 unit up. Translation P'(x,-y,z) 2 units back, 3 units left, and 1 unit up is P''(x-2,-y-3,z+1): Translation P'(x,-y,z) → P''(x-2,-y-3,z+1)
X = 13 because if NK = 23 that means the equation is x-6+9+2x-19 = 23 then you subtract 9 from each side of the equals sign and add the x’s together than add -6 to -19 and get a equation of 3x-25 = 14 then add 25 to each side and get 3x = 39 the divided 39 by 3 and get x = 13