Two points on l1 and two points on l2 are given Determine wh

Two points on l_1 and two points on l_2 are given. Determine whether l_1 is parallel to l_2, l_1, is perpendicular to l_2, or neither. l_1: (2, 0) and (0, 2); l_2: (3, 0) and (0, 3) l_1: (7, 6) and (3, 9); l_2:(5, -1)and(9, -4) l_1: (3, 2) and (-1, 2); l_2 (2, 0) and (3, -1) l_1: (4, 6) and (5, 7); l_2: (-1, -1) and (1, 4) l_1: (3, 5) and (9, 1); l_2: (4, 0) and (6, 3)

Solution

#(16) Given :

L1 = ( 7,6) and (3,9)

L2 = ( 5,-1) and ( 9, - 4)

Need to determine the slopes of L1 and L2. Let m1 be the slope of L1 and m2 be the slope of L2.

Note 1: The lines are perpendicular if the product of the slopes is equal to -1.

Note 2: The lines are parallel if the slopes are equal.

Note 3: And neither if it does not satisfy Notes 1 and 2 above.

Slope of Line 1( L1)is given as : ( 7,6) and (3,9)

hence, x1 = 7, y1 = 6, x2 = 3, y2 = 9

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

so, plug in the L1, we get:

m = ( 9 - 6 ) / ( 3 - 7)

= 3/ -4

Hence, m1 = - 3/4

Now,

Slope of Line 2( L2)is given as :

L2: ( 5,-1) and ( 9, - 4), then let x1 = 5, y1 = -1 , x2 = 9, and y2 = - 4

so, slope m2 = ( - 4 - (-1) ) / ( 9 - 5 )

                 = ( - 4 + 1) / 4

= - 3/4

Hence, m2 = - 3/4

Now,

we find the product of m1 and m2 , we get:

(-3/4) * (-3/4) = 9/16

Since the product of m1 and m2 is not equal to -1, so they are not perpendicular.

Since slope m1 and m2 are equal (-3/4) , hence they are parallel.

Hence the lines are parallel . [ Answer ]