Home > Geometry > Reflections

What is the image of (6, -3) reflected over the line y=4?

Answer 1

Aaliyah Anderson

Coordinates of image are #(6,11)#

As #y=4# is parallel to #x#-axis,

abscissa of image would not change and will be #6#.

Further distance of #(6,-3)# from #y=4# is #|-3-4|=7# and point is below line #y=4#

hence image will be further #7# from it and hence

its ordinate would be #4+7=11# and

Coordinates of image are #(6,11)# graph{((x-6)^2+(y-11)^2-0.1)((x-6)^2+(y+3)^2-0.1)(y-4)=0 [-16.58, 23.42, -4.96, 15.04]}

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Avery Allen

To find the image of a point reflected over a line, you can use the formula for reflecting a point over a line. The formula is:

[ (x', y') = (x, -y + 2b) ]

Where:

((x', y')) is the image point
((x, y)) is the original point
(b) is the y-intercept of the line of reflection

Given that the line of reflection is (y = 4), its y-intercept ((b)) is 4.

Now, substitute the values (x = 6), (y = -3), and (b = 4) into the formula:

[ (x', y') = (6, -(-3) + 2 \cdot 4) ]

[ (x', y') = (6, 10) ]

So, the image of the point (6, -3) reflected over the line (y = 4) is (6, 10).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.