The sides AB and AC of a triangle lies on the lines 2x-y=5 and x+3y =13 respectively. Given that C is the point (-2, 5) and that ABC=90°, what are the coordinates of A and B?

Answer 1

Unfortunately this application does not have graphic capability. so you'll have to get out your graphic paper

and follow along.

Point B is given by the point where these two lines intersect. Also note the second line equation can be written

as y = -1/3 x + 13/3 Equating these two equations we have: 2x - 5 = -1/3x + 13/3 Multiplying both sides

by 3 yields

6x - 15 = -x + 13 or 7x = 28 so x 4, substituting for x we find y = 3

So he coordinates of B are (4,3). If you are following your drawing you will see that point A is

where the 2x - y = 5 intersects the y axis. So substitute y = 0 into this equation & find x = 2 1/2

So the coordinates of point B are (2 1/2,0)

Answer 2

First, graph the two lines to get some sense of what's going on.

Answer 3

First, graph the two lines to get some sense of what's going on.

Answer 4

If ABC is 90 degrees then AB is perpendicular to BC and their slopes will be negative reciprocal.

We are given that AB is on 2x-y=5

Add the y to both sides and subtract the 5 from both sides yields y = 2x-5 so the slope of AB is 2. Therefore the slope of BC is -1/2.

If you draw the line of the equation y=2x-5 then plot the point (-2,5) you can easily find B by going down 1 right 2 three times. You end up at the point (4,2)

Taking the line AC is on x+3y=13 subtract the x from both sides then divide both sides by 3

Y =(-1/3)x+13/3

To find A start at point C and go down one right 3 twice. It intersects with the line AB lies on at (4,3) which is A