Question

The diagram shows points A, B and C lying on the line 2y = x + 4.?

The point A lies on the y-axis and AB = BC. The line from D(10, -3) to B is perpendicular to AC. Calculate the coordinates of B and C.

Answer 1

Step 1:

A, B, and C are the points lying on the line .

Since the point A lies on the y - axis, Substitute in the line equation.

Thus, the point A is .

Step 2:

The line from to  B is perpendicular to AC .

Which means that the line BD is perpendicular to AC .

Find the slope of the line AC .

The line equation is .

Write the equation in slope - intercept form of line equation , where m is slope and b is the y - intercept.

.

Compare the equation with .

Slope is .

Since the slopes of the perpendicular lines are negative reciprocals, slope of the line AC is .

Step 3:

Find the line BD.

Point-slope form of line equation is , where m is the slope and is the point lies on the line.

Substitute the point and in above equation.

Step 4:

Point B is the intersection point of the lines AC and BD .

Substitute in .

If , then .

Thus, the point B is .

Step 5:

Since AB = BC , point B is the mid point of AC .

Let the points are , , and .

Mid point .

Equate the x and y coordinates.

Thus, the point C is .

Solution:

The points B and C are and .