Question

Can someone solve this for me? An explanation of all translation rules would be very much appreciated as well!

Answer 1

(x+10, y+8)

Explanation:

Take the original coordinates (-7,-3) and subtract then from the prime coordinates (3,5).

x value: 3 - (-7) = 10

y value: 5 - (-3) = 8

This can be repeated with the coordinate B in order to check.

Answer 2

(x, y) → (x + 10, y + 8)

Explanation:

A translation is a rigid transformation that moves all points of a figure the same distance in the same direction without changing their orientation or shape.

In this context, the line segment
`\overline{\sf B'C'}` is a translation of the line segment
`\overline{\sf BC}`, with the following endpoints:

• B (-6, -7) and C (-7, -3)
• B' (4, 1) and C' (3, 5).

To determine the translation rule that relates the line segment
`\overline{\sf B'C'}` to
`\overline{\sf BC}`, we can find the horizontal and vertical shifts by comparing the corresponding endpoints.

Horizontal shift

• Point B' is 10 units to the right of point B.
• Point C' is 10 units to the right of point C.

Therefore, there is a horizontal shift of 10 units to the right, which can be expressed as (x + 10).

Vertical shift

• Point B' is 8 units above point B.
• Point C' is 8 units above point C.

Therefore, there is a vertical shift of 8 units up, which can be expressed as (y + 8).

Hence, the mapping rule for this translation is:

`\large\boxed{\boxed{(x, y) \rightarrow (x + 10, y + 8)}}`