Question

the line passing through the points (-2,12) and (3, -23) intersects the line passing through which of these pairs of points

Answer 1

Options (1), (2) and (3)

Explanation:

To solve this problem we will use the property,

"A system of equations will have a unique solution if slopes of the linear equations are different"

Slope of a line passing through two points
`(x_1,y_1)` and
`(x_2,y_2)` =
`(y_2-y_1)/(x_2-x_1)`

Slope of a line passing through (-2, 12) and (3, -23) =
`(12+23)/(-2-3)` = (-7)

Option (1)

Slope of a line passing through (-4, 17) and (5, -28) =
`(17+28)/(-4-5)` = (-5)

Option (2)

Slope of a line passing through (-2, 16) and (2, -20) =
`(16+20)/(-2-2)` = (-9)

Option (3)

Slope of a line passing through (-6, 14) and (4, -16) =
`(14+16)/(-6-4)` = (-3)

Option (4)

Slope of a line passing through (-3, 19) and (6, -44) =
`(19+44)/(-3-6)` = (-7)

Option (5)

Slope of a line passing through (-5, 32) and (3, -24) =
`(32+24)/(-5-3)` = (-7)

Slopes of options (1), (2) and (3) are different.

Therefore, Options (1), (2) and (3) will be the correct options.