Select the correct answer. AB and BC form a right angle at point B. If A = (-3, -1) and B = (4, 4), what is the equation of BC?
A. x + 3y = 16
B. 2x + y = 12
C. -7x − 5y = -48
D. 7x − 5y = 48

The answer to your question the equation of the line BC is C

Since AB and BC form a right angle at point B, it means that AB is perpendicular to BC.

To find the equation of BC, we first need to find the gradient of BC.

Let m be the gradient of AB and m' be the gradient of BC, since AB is perpendicular to BC, mm' = -1. Thus m' = -1/m

So, we need to find the gradient of AB and thus find the gradient of BC.

To find the gradient of AB, we use the equation for the gradient of a line in slope-point form. Having point A = (x₁, y₁) = (-3, -1) and point B = (x₂, y₂) = (4, 4).

Substituting the values of the variables into the equation, we have

Since m' = -1/m

m' = -1 ÷ 5/7

m' = -7/5

Since we know the gradient of the line BC and the line BC passes through the point B = (4, 4) = (x₂, y₂) we find the equation of the line BC using the equation of a line in slope-point form.

cross-multiplying, we have

Expanding the brackets, we have

Subtracting 28 from both sides, we have

Subtracting 5y from both sides, we have

So, the equation of the line BC is

The answer to your question the equation of the line BC is C

Learn more about the equation of a line here:

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it is the most commonly accepted one