Answer:
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!!!
