In the xy-coordinate plane, the coordinates of point A are (4,3)....

Question

In the xy-coordinate plane, the coordinates of point A are (4,3). If point B is the reflection of point A over the x-axis and point C is the reflection of point B over the y-axis, then point C is the reflection of point A over what line? The answer is line y=-4x/3 but I'm not sure how they produced that.

 

 

The multiple choice list was

• the line y=-4x/3
• the line y=-x
• the line y=x
• the x-axis
• the y-axis

Answer 1

Point A = (4, 3)

Point B = (4, -3)

Point C = (-4, -3)

 

 

Compare Point C to point A.

 

Point A is in the 1st quadrant.  Point C is the 3rd quadrant.  These points are a reflection over a line with a negative slope.

 

The line you want is

 

y = -x

Answer 2

The reflection of (4,3) over x axis means B = (4,-3)

The reflection of (4,-3) over y axis means C = (-4,-3)

 

So we are looking at   A = (4,3)  and   C = (-4,-3)

This is a reflection over the line y = -x

 

I don't know how they got an answer of reflecting over y = -4x/3

 

Take a look at:  http://hotmath.com/hotmath_help/topics/reflections.html

 

<<<<<<<<The above answer is incorrect>>>>>>>

 

The reflection of (4,3) over y=-x would be (-3,-4)  but we are reflecting

from (4,3) to (-4,-3)

 

To find the line of reflection we need the equation of the line perpendicular to the

line through the given points that runs through the midpoint of the two given points.

 

The slope between (4,3) and (-4,-3) is  (-3-3)/(-4-4) = 6/8 = 3/4

The perpendicular slope is m = -4/3

 

The midpoint of (4,3) and (-4,-3) is   ((4-4)/2, (3-3)/2) = (0,0)

 

The line of reflection must have slope m=-4/3 and run through (0,0)

 

Using point slope form we have   y-y₁ = m(x-x₁)

                                               y-0 = -4/3(x-0)

                                               y = -4/3 x

 

The line of reflection between (4,3) and (-4.-3) is  y = -4/3 x