Question

Given the point P(5, 4) and the translation f(x,y)=(x+2,y+2), what are the coordinates of P′?

a) P′ (7,6)

b) P′(5,4)

c) P′(3,2)

d) P′(7,4)

Answer 1

By applying the translation f(x, y) = (x+2, y+2) to point P(5, 4), we find the new coordinates for P' to be (7, 6), which corresponds to option (a).

Step-by-step explanation:

Given the point P(5, 4) and the translation f(x,y) = (x+2, y+2), we can find the coordinates of P' by simply adding 2 to both the x and the y coordinates of point P. The calculation is as follows:

• P's x-coordinate: 5 + 2 = 7
• P's y-coordinate: 4 + 2 = 6

To find the coordinates of P', we need to apply the translation function f(x,y)=(x+2,y+2) to the coordinates of point P(5, 4).

Using the translation function, we add 2 to the x-coordinate and 2 to the y-coordinate of P:

x' = 5 + 2 = 7

y' = 4 + 2 = 6

Therefore, the coordinates of P' are (7, 6).

Thus, the coordinates of P' after the translation are (7, 6). Therefore, the correct answer is (a) P' (7,6).