Straight Line Geometry question?

Question

ABCD is a rectangle with A (7,1) and B (3,4). C is the point (8, k)

How would you work out the value of k?

I've found out that the gradient of AB is 3/-4. What would the gradient of BC be?

Answer 1

Step 1:

Rectangle has coordinate points and .

Gradient of the line joining the point is .

Since line joining the point and is perpendicular.

Thus, the gradient of the line joining the point is .

gradient is .

General form of line equation is .

The line equation is .

Substitute in to find .

Substitute in the line equation.

.

Step 2:

Find value.

Substitute in the .

Solution :

The value of is .