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Ipatiy [6.2K]
3 years ago
15

AB and BC form a right angle at point B if A = (-3,-1) and B = (4,4) what is the equation if BC

Mathematics
1 answer:
sergejj [24]3 years ago
5 0

Answer:

7x+5y-48=0

Step-by-step explanation:

Refer the attached figure .

We are given a line AB

Point A=(x_1,y_1) = (-3,-1)

Point B=(x_2,y_2) = (4,4)

Formula for slope 'm' when two points are given :

m=\frac{y_2-y_1}{x_2-x_1}

Substituting thew values

m=\frac{4-(-1)}{4-(-3)}

m=\frac{5}{7}

Since we are given that AB is perpendicular to BC

So, By property - perpendicular slopes are negative reciprocals of each other.

\Rightarrow m_1\times m_2 =-1

\Rightarrow \frac{5}{7}\times m_2 =-1

\Rightarrow m_2 = \frac{-7}{5}

So, Slope for line BC : m_2 = \frac{-7}{5}

Point B = (4,4)

Formula of equation of line : y-y_1=m(x-x_1)

y-4=\frac{-7}{5}(x-4)

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

5y-20=-7x+28

7x+5y-20-28=0

7x+5y-48=0

Hence the equation of line BC : 7x+5y-48=0

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