Question

The line passing through the points (-2, 12) and (3, -23) intersects the line passing through which of these pairs of points? Select three that apply,

(-3, 19) and (6.-44)
(-5,32) and (3.-24)
(-4, 17) and (5.-28)
(-6, 14) and (4.-16)
(-2.16) and (2.-20)

Answer 1

(–4, 17) and (5, –28)

(–6, 14) and (4, –16)

(–2, 16) and (2, –20)

Explanation:

Answer 2

(-4, 17) and (5.-28)

(-6, 14) and (4.-16)

(-2.16) and (2.-20)

Explanation:

we know that

If two lines intersect, then their slopes are different

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

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

Find the slope of the given line

points (-2, 12) and (3, -23)

substitute in the formula

`m=(-23-12)/(3+2)`

`m=(-35)/(5)`

`m=-7}`

Verify each case

case 1

(-3, 19) and (6.-44)

substitute in the formula

`m=(-44-19)/(6+3)`

`m=(-63)/(9)`

`m=-7`

Compare with the slope of the given line

`-7=-7`

The slopes are the same

therefore

The lines not intersect because are parallel lines

case 2

(-5,32) and (3.-24)

substitute in the formula

`m=(-24-32)/(3+5)`

`m=(-56)/(8)`

`m=-7`

Compare with the slope of the given line

`-7=-7`

The slopes are the same

therefore

The lines not intersect because are parallel lines

case 3

(-4, 17) and (5.-28)

substitute in the formula

`m=(-28-17)/(5+4)`

`m=(-45)/(9)`

`m=-5`

Compare with the slope of the given line

`-5 \\eq -7`

The slopes are different

therefore

The lines intersect

case 4

(-6, 14) and (4.-16)

substitute in the formula

`m=(-16-14)/(4+6)`

`m=(-30)/(10)`

`m=-3`

Compare with the slope of the given line

`-3 \\eq -7`

The slopes are different

therefore

The lines intersect

case 5

(-2.16) and (2.-20)

substitute in the formula

`m=(-20-16)/(2+2)`

`m=(-36)/(4)`

`m=-9`

Compare with the slope of the given line

`-9 \\eq -7`

The slopes are different

therefore

The lines intersect