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

User Razboy
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1 Answer

3 votes

Answer:

the equation of line BC is y = (-7/5)x + (48/5).

Explanation:

To find the equation of the line that passes through points B and C, we first need to determine the coordinates of point C. Since the angle at B is a right angle, we can use the slope of line AB to find the slope of line BC.

The slope of line AB is:

mAB = (yB - yA) / (xB - xA)

= (4 - (-1)) / (4 - (-3))

= 5/7

Since lines AB and BC are perpendicular, the slope of line BC is the negative reciprocal of the slope of line AB:

mBC = -1 / mAB

= -7/5

Now we can use the point-slope form of the equation of a line to find the equation of line BC. We can use point B as the known point, since we already know its coordinates:

y - yB = mBC(x - xB)

Substituting the values we have:

y - 4 = (-7/5)(x - 4)

Expanding and simplifying:

y - 4 = (-7/5)x + (28/5)

y = (-7/5)x + (48/5)

User Saad Aleem
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