Determine whether line AB and line CD are parallel, perpendicular, or neither. A(-6,-9), B(8,19), C(0,-4), D(2,0) Responses

Answer 1

AB and CD both have a slope of 2

(19+9)/(8+6) = 28/14 =2 = AB's slope

(0+4)/(2-0) = 4/2 = 2 = CD's slope

If they have the same slope, they are parallel lines

for CD y = 2(x-2) or y=2x-4

equation for AB has a different y intercept: y+9=2(x+6) or y= 2x +3

they have different y intercepts, but the same slope. They're parallel

Had they been with the same slope and the same y intercept, they'd be identical lines, and not parallel.

Parallel lines don't intersect. The same identical lines coincide at every point.

Answer 2

Use your knowledge of the slopes of two lines:

Parallel lines have the same slope.

Perpendicular line have slopes that are the negative reciprocals of each other.

Then, there is neither.

Use the two-point form of the equation of a line:

(y-y₁) = ( (y₂ - y₁) / (x₂-x₁) ) ( x - x₁)

Then convert to slope-intercept form (y=mx+b) and look at the slope m.

For line AB:

(y - (-9)) = ( (19 - (-9) ) / ( 8 - (-6) ) ) (x - (-6))

y + 9 = ( (28/14) ) ( x+6)

y + 9 = 2x + 12

y = 2x + 3

For line CD:

(y-(-4)) = ( (0-(-4)) / (2-0) ) ( x - 0)

y + 4 = ( 4 / 2 ) x

y = 2x - 4

Now, consider the slopes ( 2 and 2). Are the lines parallel, perpendicular, or neither ?

You could shorten this solution by just calculating the slope: (y₂ - y₁) / (x₂-x₁)

Answer 3

Slope of line AB m_AB = (19 + 9)/(8 + 6) = 2; slope line CD m_CD = (0 + 4)/(2 - 0) = 2.

So, lines are parallel