Ab and bc form a right angle at point b. if a = (-3, -1) and b = (4, 4), what is the equation of bc?

Equation of BC: 7x + 5y = 48.

Step-by-step explanation:

It is mentioned that lines AB and BC form a 90 degree angle at point B, which means that these 2 lines are perpendicular. This implies that the product of the gradients of the lines AB and BC is -1. It is given by:

(m of AB)*(m of BC) = -1

(m of BC) = -1/(m of AB). This is the negative reciprocal of the gradient.

In order to find the equation of the line BC, first find the gradient of AB.

m of AB = (y2 - y1)/(x2-x1).

It is given that A = (x1, y1) = (-3, -1) and B = (x2, y2) = (4, 4). Plugging in the values in the gradient formula:

m of AB = (4 - (-1))/((4 - (-3)) = (4+1)/(4+3).

m of AB = 5/7.

By the perpendicular relationship, the gradient of BC is the negative reciprocal of the gradient of AB. Therefore, m of BC = -7/5.

The equation of BC can be calculated since m = -7/5 and B = (x1, y1) = (4, 4) is given. Equation of line is given by the following formula:

(y - y1) = m*(x - x1).

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

5y-20 = -7x+28.

7x + 5y = 48.

Therefore, the equation of the line BC is 7x + 5y = 48!!!

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