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

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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.
asked Feb 9, 2015 in PRECALCULUS by anonymous
reshown Feb 9, 2015 by goushi

1 Answer

0 votes

Step 1:

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

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

image

Thus, the point A is image.

Step 2:

The line from image 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 image.

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

image.

Compare the equation with image.

Slope is image.

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

Step 3:

Find the line BD.

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

Substitute the point image and image in above equation.

image

Step 4:

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

Substitute image in image.

image

If image, then image.

Thus, the point B is image.

Step 5:

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

Let the points are image, image, and image.

Mid point image.

image

Equate the x and y coordinates.

image

Thus, the point C is image.

Solution:

The points B and C are image and image.

answered Feb 9, 2015 by lilly Expert
edited Feb 9, 2015 by lilly

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