Question

Points A and B coordinates (3, 2)and (-1, 4) respectively,?

(i) Find the equation of the straight line which is perpendicular to AB and which passes through its mid-point.
(ii) Verify that the point C with coordinates (0, 1) lies on this line, and calculate the area of the triangle ABC.

Answer 1

Step 1:

(i)

The points are and .

The slope of two pints is .

The points are and .

The slope of is .

The slope perpendicular to is .

Substitute in .

The slope perpendicular to is .

Step 2:

The mid point of is

The line equation passes through the point and slope is .

The slope intercept form  .

Substitute  and slope is .

The line equation is .

Solution:

The line equation is .

Answer 2

Step 1:

(ii)

The point is .

The line equation is .

Substitute in .

The satisfies the equation.

so, lies on the .

Step 2:

The points of triangle are , and .

The base of triangle is .

The height of the triangle is the distance between mid point of and .

The mid point of is

The height of the triangle is

The area of triangle is .

Substitute and .

The area of triangle is square units.

Solution:

The area of triangle is square units.