Point T is at (−6, 4). What are the coordinates of point T" after LaTeX: R_{y-axis}\circ R_{x-axis}R y − a x i s ∘ R x − a x i s?

T"(6,-4)

Step-by-step explanation:

Given the point T at T(-6,4). If the coordinate rotates about the y-axis, the new coordinates T'y is expressed as:

T(x,y) = T'y(-y,x)

This means that, x = -y and y = x

From the coordinate T(-6,4),

x = -6 and y = 4

New coordinates will be T'(-y, x)

T' = (-4, -6)

x1 = -4, y1 = -6

If the coordinates is rotated again about the x axis, the new coordinates will be (-y1,x1)

T''(-y1,x1) = T''(-(-6), -4)

T"(-y1,x1) = T"(6,-4)

Hence the coordinates of point T" after RyRx is T"(6,-4)