The equations of three lines are given below 10x4y2 2 y5x8 L

The equations of three lines are given below 10x-4y=-2 2 y=-5x-8 Line 1: Line 2: Line 3: 2y 5x+4 For each pair of lines, determine whether they are parallel, perpendicular, or neither. Line 1 and Line 2: Parallel Line 1 and Line 3: Parallel Perpendicular Neither Line 2 and Line 3: O Parallel Perpendicular Neither Perpendicular Neither

Solution

Line 1:
10x -4y =2
=>4y=10x+2
=>y=(10_/4)x+(2_/4)
=>y=(5_/2)x+(1_/2)

slope =5_/2

Line 2:
y =-(2_/5)x-8
slope=-(2_/5)

Line 3:
-2y=5x+4
=>y=-(5_/2)x -(4_/2)
=>y=-(5_/2)x -2

slope=-(5_/2)

slope of line 1 *slope of line 2 = (5_/2)*(-2_/5) =-1
product of slopes is -1
Therefore Line 1 and Line 2 are perpendicular to each other

slope of line 1 *slope of line 3 = (5_/2)*(-5_/2) =-25_/4
slope of line 1 not equal to slope of line 3
Therefore Line 1 and Line 3 are neither parallel nor perpendicular to each other

slope of line 2 *slope of line 3 = (-2_/5)*(-5_/2) =1
slope of line 2 not equal to slope of line 3
Therefore Line 2 and Line 3 are neither parallel nor perpendicular to each other

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