Determine whether AB and CD are parallel perpendicular or ne

Determine whether AB and CD are parallel, perpendicular, or neither. 41. A(-1-4),B(2, 11), C(, 1), D(4, 10) 5. 45, write an equation of the line parallel to y 8x-1 that contains (-6, 2).

Solution

Ans 41:

Step 1: Given line AB with coordinates of A(-1, -4) and that of B(2, 11)

Step 2: Given line CD with coordinates of C(1, 1) and that of D(4, 10)

Step 3: Let us calculate slopes of both these lines

Slope = m = (y₂ - y₁)/(x₂ - x₁)

Step 4: Slope of AB = m₁ = [11 - (-4)]/[2 - (-1)]

m₁ = 15/3 = 5

Step 5: Slope of CD = m₂ = [10 - 1]/[4 - 1]

m₂ = 9/3 = 3

Step 6: For 2 lines to be parallel, slopes should be same. m₁ and m₂ are not equal. So, AB and CD are not parallel

Step 7: For 2 lines to be perpendicular, product of slopes should be -1. m₁*m₂ = 5*3 = 15. Product of slopes is not -1, so lines are not perpendicular

Step 8: Hence AB and CD are neither

Ans 45:

Step 1: Given line y = 8x - 1. To find equation of line parallel to this line and containing point (-6, 2)

Step 2: We know, equation of line can be written as

y = mx + c

Parallel lines have equal slopes. Therefore, slope of line parallel to y = 8x - 1 is 8

Hence, the equation becomes

y = 8x + c

We know that this line contains point (-6, 2)

Putting y = 2 and x = -6 in above equation

2 = 8*(-6) + c

2 = -48 + c

c = 50

Therefore, the equation of parallel line is

y = 8x + 50