Question

Not sure how to do this

Answer 1

(0,-4)

Explanation:

we know that

Point C will be on a line perpendicular to segment AB that passes through the point B

step 1

Find the slope of AB

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

we have

A(2,4),B(5,-1)

substitute

`m=(-1-4)/(5-2)`

`m_A_B=-(5)/(3)`

step 2

Find the slope of the line BC perpendicular to the segment AB

Remember that

If two lines are perpendicular, their slopes are opposite reciprocal ( the product of the slopes is -1)

`m_A_B*m_B_C=-1`

we have

`m_A_B=-(5)/(3)`

therefore

`m_B_C=(3)/(5)`

step 3

Find the equation in point slope form of the line BC

`y-y1=m(x-x1)`

we have

`m=(3)/(5)`

`B(5,-1)`

substitute

`y+1=(3)/(5)(x-5)`

step 4

Verify each case

we know that

The point C must be satisfy the linear equation

Substitute the value of x and the value of y in the linear equation and compare the result

a) we have (0,-6)

substitute

`-6+1=(3)/(5)(0-5)`

`-5=-3` ----> is not true

therefore

The ordered pair is not a possible location of point C

b) we have (0,-4)

substitute

`-4+1=(3)/(5)(0-5)`

`-3=-3` ----> is true

therefore

The ordered pair is a possible location of point C

c) we have (8,6)

substitute

`6+1=(3)/(5)(8-5)`

`7=(9)/(5)` ----> is not true

therefore

The ordered pair is not a possible location of point C

d) we have (8,4)

substitute

`4+1=(3)/(5)(8-5)`

`5=(9)/(5)` ----> is not true

therefore

The ordered pair is not a possible location of point C