Question

A square with sides of length eight units, sits on a graph with its lower left hand corner at the origin (0,0). This square is translated five units up, and seven units left. What are the coordinates of the ​upper right hand corner after translation? Explain.

PLEASE HELP ME ON THIS QUESTION. I don’t understand. Only answer if you know because you will receive consequences with monitor.

Answer 1

The coordinates of the upper right hand corner after translation is (1, 13)

Explanation:

Let us revise the rules of translation

• If the point (x , y) translated horizontally to the right by h units then its image is (x + h , y) ⇒ T (x , y) → (x + h , y)

• If the point (x , y) translated horizontally to the left by h units then its image is (x - h , y) ⇒ T (x , y) → (x - h , y)

• If the point (x , y) translated vertically up by k units then its image is (x , y + k)→ (x + h , y) ⇒ T (x , y) → (x , y + k)

• If the point (x , y) translated vertically down by k units then its image is (x , y - k) ⇒ T (x , y) → (x , y - k)

At first let us find the upper right hand corner of the square

∵ Its lower left hand corner at the origin (0,0)

∵ The length of each side of the square is 8 units

→ To find lower right hand corner add 8 to the x-coordinate of the

lower left hand corner

∴ The lower right hand corner = (0 + 8, 0)

∴ The lower right hand corner = (8, 0)

→ To find upper right hand corner add 8 to the y-coordinate of the

lower right hand corner

∴ The upper right hand corner = (8, 0 + 8)

∴ The upper right hand corner = (8, 8)

Now Let us find the image of this corner after translation

∵ This square is translated five units up

→ Use the 3rd rule above

∴ Add 5 to the y-coordinate of the point (8, 8)

∴ Its image = (8, 8 + 5)

∴ Its image = (8, 13)

∵ The square is translated seven units left

→ Use the 2nd rule above

∴ Subtract 7 from the x-coordinate of the point (8, 13)

∴ Its image = (8 - 7, 13)

∴ Its image = (1, 13)

The coordinates of the upper right hand corner after translation is (1, 13)