Question

1. describe the horizontal and vertical distance required to move each point to its image.

a) a(5, - 3) to a(2, 6)
b) b(- 3, 0) to b(- 5, - 3)
c) c(2, - 1) to c(4, 3)
d) d(- 1, 2) to d(- 4, 0)
e) e(3, 3) to e(- 3, 3)
f) f(4, - 2) to f(4, 2)

Explanation:

To solve this, we use the concept of horizontal (change in \( x \)-coordinate) and vertical (change in \( y \)-coordinate) distances. The horizontal distance is \( \Delta x = x_{\text{image}} - x_{\text{original}} \) and vertical distance is \( \Delta y = y_{\text{image}} - y_{\text{original}} \). A positive value means moving right (horizontal) or up (vertical), negative means left or down.

Part (a): \( A(5, -3) \) to \( A'(2, 6) \)

Step 1: Horizontal Distance (\( \Delta x \))

\( \Delta x = 2 - 5 = -3 \) (3 units left)

Step 2: Vertical Distance (\( \Delta y \))

\( \Delta y = 6 - (-3) = 9 \) (9 units up)

Answer:

(a): Horizontal: 3 units left, Vertical: 9 units up

Part (b): \( B(-3, 0) \) to \( B'(-5, -3) \)

Step 1: Horizontal Distance (\( \Delta x \))

\( \Delta x = -5 - (-3) = -2 \) (2 units left)

Step 2: Vertical Distance (\( \Delta y \))

\( \Delta y = -3 - 0 = -3 \) (3 units down)