Translate a point (x, y) 3 units left and 5 units up. Then translate the image 5 units right and 2 units up. What are the coordinates of the point after the translations?
The coordinates are

Please check the explanation.

Step-by-step explanation:

Given the point

P(x, y)

Please note that when we translate a point 'c' units left, the 'c' units are subtracted from the x-values, and when translating a point 'c' units right, we add the 'c' units to the x-values.

Also, note that when we translate a point 'c' units down, the 'c' units are subtracted from the y-values, and when translating a point 'c' units up, we add the 'c' units to the y-values.

After First Translation:

3 units left and 5 units up

P(x, y) → P'(x-3, y+5)

After Second Translation:

Translate the image 5 units right and 2 units up.

P'(x-3, y+5)  → P''(x-3+5, y+5+2) = P''(x+2, y+7)

Thus, the coordinates  of the point(x, y) after the translations are:  P''(x+2, y+7)

TAKING AN EXAMPLE

Let us consider that point

P(0, 0)

After First Translation:

3 units left and 5 units up

P(0, 0) → P'(0-3, 0+5) = P'(-3, 5)

After Second Translation:

Translate the image 5 units right and 2 units up.

P'(-3, 5) → P''(-3+5, 5+2) = P''(2, 7)

Thus, the coordinates  of the point P(0, 0) after the translations are:

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step-by-step explanation:

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