Question

(912.GR.2.5)

ABhas endpoints at A(-3, 2) and B(3, 8). If ABwas rotated 90° clockwise about the origin and translated along the
vector<-2, -1>, what are the coordinates of A" B"?
B"

Answer 1

To rotate AB 90° clockwise about the origin, we use rotation formulas. After finding A', we can translate A' and B' along the given vector to find A'' and B''.

Step-by-step explanation:

To find the new coordinates of A' and B' when AB is rotated 90° clockwise about the origin, we can use the rotation formula. For a point (x, y) rotated counterclockwise by angle θ, the new coordinates (x', y') can be found using the following formulas:

x' = x*cos(θ) - y*sin(θ)

y' = x*sin(θ) + y*cos(θ)

For a 90° clockwise rotation, θ = -90° or -π/2 radians. Plugging in the values for A(-3, 2), we get:

x' = -3*cos(-π/2) - 2*sin(-π/2) = 2

y' = -3*sin(-π/2) + 2*cos(-π/2) = 3

So, A' has coordinates (2, 3). Following the same steps, we can find the coordinates of B'.

Now, to translate A' and B' along the vector <-2, -1>, we simply add the vector components to the x and y coordinates of each point:

A'' = (A'x + (-2), A'y + (-1)) = (2 + (-2), 3 + (-1)) = (0, 2)

B'' = (B'x + (-2), B'y + (-1)) = (?, ?)

Now we need to find the coordinates of B'.

Learn more about Rotating points, translating points