Question

Which type of lines pass through points (1, 2), (9, 9) and (0,12), (7,4) on a grid: parallel, perpendicular, or neither?

Answer 1

`"perpendicular lines"`

Explanation:

`"to compare the lines calculate the slope m for each one"`

`• " Parallel lines have equal slopes"`

`• " The product of the slopes of perpendicular lines "`
`color(white)(xxx)" is equal to - 1"`

`"to calculate the slope m use the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(1,2)" and "(x_2,y_2)=(9,9)`

`rArrm=(9-2)/(9-1)=7/8`

`"for the second pair of coordinate points"`

`"let "(x_1,y_1)=0,12)" and "(x_2,y_2)=(7,4)`

`rArrm=(4-12)/(7-0)=-8/7`

`7/8!=-8/7" hence lines are not parallel"`

`7/8xx-8/7=-1" hence lines are perpendicular"`