Question

AB and BC form a right angle at point B. If A = (-3,-1) and B = (4,4), what is the equation of BC

Answer 1

The equation of line BC, which is perpendicular to line AB, can be determined by first calculating the slope of AB and then using the negative reciprocal for BC's slope. Using point B and this slope, we derive the equation of BC: y - 4 = (-7/5)(x - 4).

Step-by-step explanation:

To find the equation of line BC given that AB and BC form a right angle at point B, we need to first determine the slope of AB and then find the negative reciprocal of that slope for the perpendicular line BC. Since point B is a common point, it will be used in the equation.

Point A is at (-3, -1) and point B is at (4, 4). The slope of line AB is calculated as follows:

mAB = (y2 - y1) / (x2 - x1)

mAB = (4 - (-1)) / (4 - (-3))

mAB = 5 / 7

The slope of line BC, being perpendicular to AB, is the negative reciprocal of 5/7, which is -7/5. Now we use point B (4,4) and the slope -7/5 to find the equation:

y - y1 = m (x - x1)

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

The equation of line BC is therefore:

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

Answer 2

`y=-1.4x+9.6`

Step-by-step explanation:

If A = (-3,-1) and B = (4,4), the slope of AB is

`\text{Slope}_(AB)=(-1-4)/(-3-4)=(-5)/(-7)=(5)/(7)`

Two perpendicular lines have slopes that have product of -1:

`\text{Slopee}_(AB)\cdot \text{Slope}_(BC)=-1\\ \\(5)/(7)\cdot \text{Slope}_(BC)=-1\\ \\\text{Slope}_(BC)=-(7)/(5)=-1.4`

The equation of the line BC with slope -1.4 and passing through the point B(4,4) is

`y-4=-1.4(x-4)\\ \\y-4=-1.4x+5.6\\ \\y=-1.4x+9.6`