Question

The triangle ABC goes through a series of transformations, resulting in the triangle A’B’C’. The three transformations are listed below. Reflection in the x- axis. Followed by a rotation of 1800 clockwise about the origin Followed by a translation 3 units down and 4 units to the right For triangle ABC, the vertex A is originally located at (-2, 3). Show the new coordinates of A after each of the three transformations above. 3 points Your answer

Answer 1

The new co-ordinates of A ( 2 ,-6)

Explanation:

Type of transformation change to co-ordinate point

Vertical translation up 'd' units (x,y)→(x , y+d)

Vertical translation down 'd' units (x,y)→(x , y-d)

Horizontal translation right 'c' units (x,y)→(x+c , y)

Horizontal translation left 'c' units (x,y)→(x-c , y)

Reflection over x-axis (x,y) →(x , -y)

Reflection over y-axis (x,y) →(-x , y)

Given the original vertex A ( -2 ,3)

a) First reflection over x-axis ( -2 ,3) →(-2 , -3)

b) Vertical translation down '3' units so it changes (-2 , -3)→(-2 , -3-3)

(-2,-3)→(-2 ,-6)

and

c) The Horizontal translation right '4' units

now it changes ( -2 ,-6) → (-2+4,-6)→(2 ,-6)

Final answer:-

The new co-ordinates of A ( 2 ,-6)