Question

Which linear equation describes the line passing through point (10,3) and has a y-intercept at (0,-1)?

Answer 1

Thus, the correct rule that represents the dilation applied to trapezoid ABCD to create A'B'C'D' is:

C.
`\( (x, y) \to (2x, 2y) \)`

The image shows a trapezoid ABCD that has been dilated to form a trapezoid A'B'C'D'. We need to determine which rule represents the dilation applied to trapezoid ABCD to create A'B'C'D'.

To find the rule, we can follow these steps:

1. Choose a Corresponding Point: Pick a point from the original figure and its corresponding point in the dilated figure.

2. Calculate Scale Factor: Determine the scale factor by comparing the distances of the chosen points from the origin.

3. Formulate the Rule: The rule for dilation with respect to the origin is given by
`\( (x, y) \to (kx, ky) \)`, where
`\( k \)` is the scale factor.

Looking at the grid in the image:

- Point B has coordinates (-2, -3).

- Point B' has coordinates (-4, -6).

The coordinates of B' are exactly double those of B, indicating that every coordinate is scaled by a factor of 2. This fits the dilation rule of
`\( (x, y) \to (2x, 2y) \).`

Thus, the correct rule that represents the dilation applied to trapezoid ABCD to create A'B'C'D' is:

C.
`\( (x, y) \to (2x, 2y) \)`

This means the rule for the dilation is to multiply both the x and y coordinates by 2, which is the scale factor for the dilation.

Answer 2

The answer for number 3 on the paper is (x, y) --- (2x, 2y)