Question

Question Graph $△ABC$△ABC​ with vertices cap A times open paren negative 4 comma negative 3 close paren$A(-4,-3)$A(−4,−3)​ , cap b times open paren 0 comma negative 2 close paren$B(0,-2)$B(0,−2)​ , and cap c times open paren 2 comma negative 2 close paren$C(2,-2)$C(2,−2)​ and and its image after a 90° clockwise rotation about point cap c$C$C​ .

Answer 1

Please find attached the graph of the triangle ΔABC and the image of the triangle after a 90° clockwise rotation about the point C created with MS Excel

What is a rotation transformation?; A rotation transformation is one in which the points on an object are rotated about a specified location.

The vertices of the triangle ΔABC are; A(-4, -3), B(0, -2), and C(2, -2)

The transformation applied to the triangle; A 90° clockwise rotation about point C

The coordinates of a point (x, y) following a rotation of 90° clockwise about the origin is; (y, -x)

Translating the point C in the triangle to the origin, we get;

C(2 - 2, -2 + 2) = A'(0, 0), therefore, the translation to the origin is a two unit translation to the left and 2 units translation upwards

Applying the translation to the vertice A and B, we get;

A(-4 - 2, -3 + 2) = A'(-6, -1)

B(0 - 2, -2 + 2) = B'(-2, 0)

The image following the rotation about point C' are therefore;

C''(0, 0), B''(0, 2), A''(-1, 6)

Translating the image to the initial position, we get;

C''(0 + 2, 0 - 2) ⇒ C'''(2, -2)

B''(0 + 2, 2 - 2) ⇒ B'''(2, 0)

A''(-1 + 2, 6 - 2) ⇒ A'''(1, 4)

Please find attached the graph of the triangle ΔABC and the image ΔA'''B'''C''' following a rotation of 90° clockwise about the point C