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Mathematics

Grade9

Easy

Question

The line s passes through the points (-6,0) and (12, 3). The line t passes through the points (-6, 7) and ( -5,1). The lines s and t are ___________lines.

Parallel
Perpendicular
Collinear
Intersecting

hint Hint:

In this question we have to find the relation between the lines. So, firstly we will find the slope of the line and then check its relation $i f space m subscript 1 equals m subscript 2 space end subscript t h e space l i n e s space w i l l space b e space p a r a l l e l comma space i f space m subscript 1 equals fraction numerator negative 1 over denominator m subscript 2 end fraction space t h e space l i n e s space w i l l space b e space p e r p e n d i c u l a r.$

The correct answer is: Perpendicular

the co-ordinates of line s is (-6,0) and (12,3)
Slope of line s, $m subscript 1$
$equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction equals fraction numerator 3 minus 0 over denominator 12 minus left parenthesis negative 6 right parenthesis end fraction equals 3 over 18 equals 1 over 6$
the co-ordinates of the line t is (-6,7) and (-5,1)
Slope of the line t, $m subscript 2$
$equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction equals fraction numerator 1 minus 7 over denominator negative 5 minus left parenthesis negative 6 right parenthesis end fraction equals fraction numerator negative 6 over denominator 1 end fraction equals negative 6$
As $m subscript 1 equals fraction numerator negative 1 over denominator m subscript 2 end fraction$
So, the lines are perpendicular.

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