Co-Ordinate Geometry Question. HARD!?

Question

The points A (-2, 4), B (6, -2) and C (5, 5) are the vertices of ABC (triangle) and D is the mid-point of AB. (D is not given). A) Find an equation of the line passing through A and B in the form ax+by+c=0, where a,b and c are intergers to be found. B) Show that CD is perpendicular to AB. WITH WORKING!!! I...

Answer 1

Step 1:

Triangle has coordinate points and .

Consider the coordinate points .

Formula for .

Substitute and in the slope formula.

Triangle slope of the line joining the point is .

General form of line equation is .

Substitute in the general form.

The line passing through the is .

Step 2:

Slope of is .

is the mid point of .

Substitute and in the mid point formula.

Point is .

Find slope of the .

Substitute and in the slope formula.

Since line joining the point is perpendicular to .

Solution :

(a) The line passing through the is .

(b) is perpendicular to .