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

the line passing through the points (-2,12) and (3, -23) intersects the line passing-example-1

1 Answer

3 votes

Answer:

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.

User Teoincontatto
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