Question

Determine whether LINE AB and LINE CD are parallel, perpendicular, or neither. A(−1, −4) , B(2, 11) , C(1, 1) , D(4, 10) ( write parallel, perpendicular, or neither

Answer 1

Step-by-step explanation:

Hey there!

The points of line AB are; (-1,-4) and (2,11).

Note:

• Use double point formula and simplify it to get two eqaution.
• Use condition of parallel lines, perpendicular lines to know whether the lines are parallel or perpendicular or nothing.

~ Use double point formula.

$(y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1)$

~ Keep all values.

$(y + 4) = \frac{11 + 4}{2 + 1} (x + 1)$

~ Simplify it.

$y + 4 = \frac{15}{3} (x + 1)$

$y + 4 = 5x + 5$

$5x - y + 1 = 0$

Therefore this is the equation of line AB.

Now, Finding the equation of line CD.

Given;

The points of line CD are; (1,1) and (4,10).

~ Using formula.

$(y - y1) = \frac{y2 - y1}{x2 - x1}(x - x1)$

~ Keep all values.

$(y - 1) = \frac{10 - 1}{4 - 1} (x - 1)$

~ Simplify it.

$y - 1 = 3 x - 3$

$3x - y - 2 = 0$

Therefore, 3x - y- 2 = 0 is the eqaution of line CD.

Use condition of parallel lines.

m1= m2

Slope of equation (i)

$m1 = \frac{ - coeff. \: of \: x}{coeff \: of \: y}$

$m1 = \frac{ - 5}{ - 1}$

Therefore, m1 = 5

Slope of second equation.

$m2 = \frac{ - coeff \: .of \: x}{coeff \: .of \: y}$

$m2 = \frac{ - 3}{ - 1}$

Therefore, m2 = 3.

Now, m1≠m2.

So, the lies are not parallel.

Check for perpendicular.

m1*m2= -1

3*5≠-1.

Therefore, they aren't perpendicular too.

So, they are neither.

Hope it helps...