Question

AB ← → and BC ← → form a right angle at point B. If A = (-3, -1) and
B = (4, 4), what is the equation of BC ← → ?


x + 3y = 16


2x + y = 12


-7x − 5y = -48


7x − 5y = 48

Answer 1

lineAB and lineBC
LineBC

Answer 2

You have to find the slope of the line AB, and then the slope of BC is the opposite reciprocal of that. Let's take a look at it...

Answer 3

The slope is found by using the slope formula for points A and B, and it is:\[m=\frac{ 4-(-1) }{ 4-(-3) }=\frac{ 5 }{ 7 }\]So the slope for the line AB is 5/7. The equation would be, using the point (4,4) and the slope of 5/7 and the point-slope formula: \[y=\frac{ 5 }{ 7 }x+\frac{ 8 }{ 7 }\]

Answer 4

so far I've gotten this far. I don't know where to go from this

Answer 5

The slope of the line BC is the opposite reciprocal of the slope of line AB, so the slope of line BC is -7/5. Use the point (4,4) andd the slope of -7/5 to write a new equation. Like this:

Answer 6

Line AB:
\[y=\frac{ 5 }{ 7 }x+\frac{ 8 }{ 7 }\]Line BC:\[y=-\frac{ 7 }{ 5 }x+\frac{ 48 }{ 5 }\]

Answer 7

Do you know how to write equations using the slope and a point on the line?

Answer 8

y=m(x-px)+py?