Question

The points represent the vertices of a triangle. (a) Draw triangle ABC in the coordinate plane, (b) find the altitude from vertex B of the triangle to side AC, and (c) find the area of the triangle.

Answer 1

Step 1 :

(a)

The three vertices of a triangle are .

1. Draw a coordinate plane.

2. Plot the three vertices of triangle.

3. Connect those vertices to form a triangle.

The triangle is shown below :

Step 2 :

(b)

Find the altitude from vertex B of the triangle to side AC :

Let the altitude is h .

First find the equation of line AC .

Let the vertices are .

Slope of AC :

Point-slope form of line equation is .

Substitute the point and the slope in the point-slope form.

The distance between the line AC and the vertices is the altitude(h ).

The altitude from vertex B of the triangle to side AC is .

Step 3 :

 (c)

Find the area of the triangle :

Area of the triangle = .

Let b be the distance between the vertices A and C .

Substitute the values in area formula.

Area of the triangle is :

Area of the triangle is .

Solution :

(a)

Graph of the triangle is :

(b) The altitude from vertex B of the triangle to side AC is .

(c) Area of the triangle is .