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

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

Step-by-step 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)

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)