Question

Answer the questions by drawing on the coordinate plane below.

a. Draw the image of ΔPQR after a rotation of 90° clockwise about the origin. Label the image ΔP’Q’R’.


b. Draw the image of ΔPQR after a reflection across the x-axis. Label the image ΔP”Q”R”.

Answer 1

Coordinates of the given triangle ΔPQR P(1,-1), Q(3,-2), R(3,-4).

a) Let us discuss the rule for rotation of 90° clockwise about the origin.

If given coordinate is (h,k) is rotated 90° clockwise about the origin the position of rotated coordinate will be (k, -h).

x and y coordinates would switch their values and after switching x any values, the y value of the coordinates would reverse in sign.

So, the coordinates of rotated ΔPQR P(1,-1), Q(3,-2), R(3,-4) would become

P(1,-1) --> P'(-1,-1)

Q(3,-2) --> Q'( -2,-3)

R(3,-4) --> R'(-4,-3)

b) If given coordinate is (h,k), the coordinates after reflection across the x-axis would besome (h,-k). (Just change in the sign of y-coordinate).

So, the coordinates of rotated ΔPQR P(1,-1), Q(3,-2), R(3,-4) would become

P(1,-1) --> P"(1,1)

Q(3,-2) --> Q"( 3,2)

R(3,-4) --> R"(3,4)