Question

PLEASE HELPP ASAP!!

5.(06.02 MC)
Line BC contains points B (4, -5) and C (3, 2). Line DE contains points D (2,0) and E (9, 1). Lines BC and DE are (1 point)
parallel
perpendicular
neither

Answer 1

Answer: Option A.

Explanation:

Hey there!

Given; The Line BC contains points B (4, -5) and C (3, 2).

And the Line DE contains points D (2,0) and E (9, 1)

Note: Use double point formula for finding the equation and then find slopes of both then put the condition for perpendicular lines and parallel lines.

From line BC;

The points are B (4, -5) and C (3, 2).

Using double point formula;

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

Keep all the value;

`(y + 5) = (2 + 5)/(3 - 4) (x - 4)`

Simplify it;

`y + 5 = - 7x + 28`

Therefore, the equation is y = -7x+23........(I)And slope(m1) is -7 {comparing the equation (I) with y=Mx+c}

Again;

The points D (2,0) and E (9, 1)

Using double point formula;

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

Keep all values;

`(y - 0) = (9 - 2)/(1 - 2) (x - 2)`

`y = - 7x + 14`

Therefore, the equation is y = -7x+14......(ii)And the slope (m2) is -7. {comparing the equation (ii) with y= mx+c}

Check:

For parallel lines:

m1= m2

-7 = -7 (true)

Therefore, the lines are parallel.

Hope it helps!