Answer:
Length of AB = 4.4721
Equation of line BC: y = -2x + 6
Step-by-step explanation:
To find the length of the line AB, we just need to find the distance between the points A and B.
We can find distance with the equation:
[tex]distance = \sqrt{(x_A - x_B)^2 + (y_A - y_B)^2}[/tex]
[tex]distance = \sqrt{(-3 - 1)^2 + (2 - 4)^2}[/tex]
[tex]distance = 4.4721[/tex]
To find the equation of the line BC, first let's find the slope of the line AB.
This slope is given by:
[tex]m_{AB} = \frac{ y_A - y_B }{ x_A - x_B }[/tex]
[tex]m_{AB} = \frac{ 2 - 4 }{ -3 - 1} = \frac{1}{2}[/tex]
The line AB is perpendicular to the line BC (because mB = 90°), so the slope of line BC is:
[tex]m_{BC} = -\frac{1}{m_{AB}} = -2[/tex]
so the line BC is:
[tex]y = -2x + b[/tex]
To find the value of b, we can use the point B (1,4):
[tex]4 = -2 + b[/tex]
[tex]b = 6[/tex]
So we have:
[tex]y = -2x + 6[/tex]
