Geometry Question

Strongt wrote:The line represented by equation y=x is the perpendicular bisector of line segment AB. If A has the coordinates (-3,3), what are the coordinates of B?

answer is [spoiler](3,-3)[/spoiler]

would someone please explain the concept behinde the answer

To bisect means to CUT IN HALF.
To be perpendicular means to FORM A RIGHT ANGLE.
Draw the figure.
Look for special triangles.



In the figure above are two 45-45-90 triangles, each with sides 3-3-3√2.
B = (3,-3).

Now that Mitch has already solved it using the concept of triangles, I will try to solve it using equation of line

Let y = mx + c ( m = slope and c = y intercept) be the equation of the line containing the line segment AB,

Slope of the line y=x is 1
Slope of the line y = mx + c is m
m*1 = -1 (product of slopes of perpendicular lines is equal to -1)
m = -1

Now the equation of line is y = -x + c.We know that point (-3,3) lies on this line. So, substituing the values of x and y in the equation y = -x + c (3 = -(-3)+ c.) we get, c = 0 . The equation of the line is now y = -x.

The reflection of (-3,3) over y = -x(infact over origin) is (3,-3)

p.s: The reflection of point (a,b) over origin is (-a,-b)

if you have choices, you can find the mid point and can check whether it is present on x=y or not.

This is just solving using choices.

user123231