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:

Answer: Option A.

Step-by-step 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;

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

Keep all the value;

$(y + 5) = \frac{2 + 5}{3 - 4} (x - 4)$

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;

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

Keep all values;

$(y - 0) = \frac{9 - 2}{1 - 2} (x - 2)$

$y = - 7x + 14$

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!