Show that the line containing the point (a, b) and (b, a) is perpendicular to the line y = x.

Also show that the midpoint of (a, b) and (b, a) lies on the line y = x.

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- Jan 16th 2007, 01:48 PMsymmetryLine Prove
Show that the line containing the point (a, b) and (b, a) is perpendicular to the line y = x.

Also show that the midpoint of (a, b) and (b, a) lies on the line y = x. - Jan 16th 2007, 02:02 PMSoroban
Hello, symmetry!

I must assume that you are familiar with the basic concepts needed:

. . slopes, perpendicular slopes, midpoints.

If you are not, learn or re-learn the formulas and concepts.

Quote:

Show that the line containing the points and

is perpendicular to the line:

The slope of the line through and is: .

The slope of the line is: .

Since

Quote:

Show that the midpoint of and lies on the line

The midpoint is: .

The two coordinates of the midpoint are equal.

. . Therefore, they satisfy the equation

- Jan 16th 2007, 05:22 PMsymmetryok
I greatly appreciate your replies and detail explanation.