The vertices of a triangle are P(-3,8), Q(-6,-4), and R(1,1). Name the vertices of the image reflected in the X-axis

- The reflection of any point ( x , y ) in a cartesian coordinate system can be determined by the units of y. The number of units of y above or below the x-axis must be determined.

- If the point ( x , y ) lies y units above the x-axis then its reflection in X-axis is y units below the x-axis while the x-coordinate remains the same. Similarly, If the point ( x , y ) lies y units below the x-axis then its reflection in X-axis is y units above the x-axis while the x-coordinate remains the same.

- We have the following vertices of the triangle:

P ( -3 , 8 ) Q ( -6 , -4 ) R ( 1 , 1 )

We see that point P lies y = 8 units then its reflection in X-axis is 8 units below the x-axis i.e y = -8 while x remains the same at x = -3. So the reflected point P' is:

P' ( - 3 , - 8 )

We see that point Q lies 4 units below x-axis y = -4 then its reflection in X-axis is 4 units above the x-axis i.e y = +4 while x remains the same at x = -6. So the reflected point Q' is:

Q' ( - 6 , 4 )

We see that point R lies y = 1 units then its reflection in X-axis is 1 units below the x-axis i.e y = -1 while x remains the same at x = 1. So the reflected point R' is:

R' ( 1 , - 1 )

- The the vertices of the reflected image are:

P' ( - 3 , - 8 ) Q' ( - 6 , 4 ) R' ( 1 , - 1 )