## anonymous one year ago (Please Help will FAN and Medal!) ←→ ←→ AB and BC form a right angle at point B. If A = (-3, -1) and ←→ B = (4, 4), what is the equation of BC?

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1. anonymous

A.) x + 3y = 16 B.) 2x + y = 12 C.) -7x − 5y = -48 D.) 7x − 5y = 48

2. anonymous

Its my final question

3. mathstudent55

|dw:1435677378715:dw|

4. mathstudent55

Look at line AB. You know two points it goes through, so you can find its slope. |dw:1435677554492:dw|

5. mathstudent55

Once you know the slope of line AB, you can find the slope of its perpendicular. The slopes of perpendiculars are negative reciprocals. Then you will know the slope of line BC and a point it goes through, B(4, 4). That is enough information to find the equation of line BC.

6. anonymous

Okay thank you!

7. anonymous

is C (6,2)?

8. anonymous

nevermind i got it Thank you for all your help!

9. anonymous

C.) -7x − 5y = -48 was the answer ^.^

10. mathstudent55

1. Find the slope of line AB using points A(-3, -1) and B(4, 4). $$slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{4 - (-1)}{4 - (-3)} = \dfrac{4 + 1}{4 + 3} = \dfrac{5}{7}$$ 2. Find the slope of the perpendicular, line BC: The slopes of perpendicular lines are negative reciprocals. That means their product is -1. That also means each one is the negative reciprocal of the other. $$slope~of~line~AB = \dfrac{5}{7}$$ $$slope~of~line~BC = -\dfrac{7}{5}$$ 3. Line BC has slope $$-\dfrac{7}{5}$$ and passes through point (4, 4) $$y = mx + b$$ $$y = -\dfrac{7}{5}x + b$$ Use point (4, 4) to find b: $$4 = -\dfrac{7}{5} \times 4 + b$$ $$4 = -\dfrac{28}{5} + b$$ $$\dfrac{20}{5} = -\dfrac{28}{5} + b$$ $$\dfrac{48}{5} = b$$ $$b = \dfrac{48}{5}$$ The equation of the line is: $$y = -\dfrac{7}{5} x + \dfrac{48}{5}$$ Multiply both sides by 5: $$5y = -7x + 48$$ Add 7x to both sides: $$7y + 5x = 48$$ If you multiply this equation by -1 on both sides, you do get -7x - 5y = -48 which is your answer.