Question

Given that the triangle ABC is at A = ( - 1, 5 ) B = ( 1, 1 ) C = ( 2, 3 ), and if the triangle is reflected across the line x = 4, find the new position of point C'.

Answer 1

Given:

The triangle ABC is at A = ( - 1, 5 ) B = ( 1, 1 ) C = ( 2, 3 ), and if the triangle is reflected across the line x = 4.

Required:

To find the new position of point C'.

Step-by-step explanation:

The coordinate point of C is (2,3).

Now, we should reflect point C with respect to the line x=4, let the reflected point coordinates be (h,k).

Since C is reflected with respect to line x= 4 which is parallel to y-axis, So the y -coordinate will be same.

Moreover, the midpoint of C and reflected point (h,k) lies on line 4.

Therefore,

`\begin{gathered} (h+2)/(2)=4 \\ \\ h+2=8 \\ \\ h=8-2 \\ \\ h=6 \\ \\ k=3 \end{gathered}`

Therefore the reflected point is (6,3)

Final Answer:

The coordinate point os c' is

`(6,3)`