Reflect triangle ABC over the y-axis and then rotate triangle 90° clockwise around the center. Plot triangle DEF.
Point B is (2,6)
point A (2,3
point c is (4,3)
To reflect triangle ABC over the y-axis, we change the sign of the x-coordinates to get the new coordinates for triangle A'B'C':
Point B' = (-2,6)
Point A' = (-2,3)
Point C' = (-4,3)
To rotate triangle A'B'C' 90° clockwise around the center, we use the following rotation matrix:
|cos(θ) -sin(θ)|
|sin(θ) cos(θ)|
Since we are rotating 90° clockwise, θ = -90° = -π/2 radians. The rotation matrix becomes:
|0 1|
|-1 0|
Rotating each of the points A'B'C' using this rotation matrix, we get the new coordinates for triangle DEF:
Point D = (-6,2)
Point E = (-3,2)
Point F = (-3,4)
Therefore, the new triangle DEF, after reflecting and rotating triangle ABC, is plotted with point D (-6,2), E (-3,2), and F (-3,4).