Question

The points A(-3, 2) and B(1,4) are vertices of an isosceles triangle ABC, where angle B = 90°

Answer 1

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:

$distance = \sqrt{(x_A - x_B)^2 + (y_A - y_B)^2}$

$distance = \sqrt{(-3 - 1)^2 + (2 - 4)^2}$

$distance = 4.4721$

To find the equation of the line BC, first let's find the slope of the line AB.

This slope is given by:

$m_{AB} = \frac{ y_A - y_B }{ x_A - x_B }$

$m_{AB} = \frac{ 2 - 4 }{ -3 - 1} = \frac{1}{2}$

The line AB is perpendicular to the line BC (because mB = 90°), so the slope of line BC is:

$m_{BC} = -\frac{1}{m_{AB}} = -2$

so the line BC is:

$y = -2x + b$

To find the value of b, we can use the point B (1,4):

$4 = -2 + b$

$b = 6$

So we have:

$y = -2x + 6$