Find the coordinates of B, and hence show that one of the two lines is perpendicular to AB.

Question

The point A has coordinates (7, 4). The straight lines with equations x + 3y + 1 = 0 and 2x + 5y = 0 intersect at the point B.? Find the coordinates of B, and hence show that one of the two lines is perpendicular to AB.

Answer 1

Step 1:

The point .

The line equations are

Solve for .

Substitute in .

Multiply each side with negative one.

.

Substitute in .

The intersecting point of and is .

Step 2:

The slope of and is .

Substitute and in .

The slope of is

The slope of line is .

The slope of is .

 

The product of two slopes is , then those lines are perpendicular.

The line and are perpendicular.

Solution:

The intersecting point is .

The line and are perpendicular.