Question

PLEEASE HELP TIMED!!!!
1) The given line segment has a midpoint at (3, 1).
On a coordinate plane, a line goes through (2, 4), (3, 1), and (4, negative 2).

What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?

y = 1/3x
y = 1/3x – 2
y = 3x
y = 3x − 8

2)The given line passes through the points (0, ) and (2, 3).
On a coordinate plane, a line goes through (0, negative 3) and (2, 3). A point is at (negative 1, negative 1).

What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (-1,-1)?
y+1=-3(x+1)
y+1+-1/3(x+1)
y+1=1/3(x+1)
y+1=3(x+1)

Answer 1

Question 1: Option B: $y=\frac{1}{3}x -2$

Question 2: Option D: $y+1=3 (x+1)$

Solution:

Question 1:

The point on the given line are (2, 4) and (4, –2).

Slope of the given line:

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{-2-4}{4-2}$

m = –3.

Slope of perpendicular line = –1 ÷ Slope of the given line

Slope of perpendicular line = $\frac{1}{3}$

Perpendicular line passing through the point (3, 1).

Slope -intercept form using point slope formula,

$y-y_1=m(x-x_1)$

$y-1=\frac{1}{3} (x-3)$

$y-1=\frac{1}{3} x-1$

$y=\frac{1}{3}x -2$

Option B is the correct answer.

Question 2:

The point on the given line are (0, –3) and (2, 3).

Slope of the given line:

$m=\frac{3+3}{2-0}$

$m=\frac{6}{2}$

m = 3.

Slope of parallel lines are equal.

Slope of parallel line =3

parallel lines passing through the point (–1, –1).

Point slope formula:

$y-y_1=m(x-x_1)$

$y+1=3 (x+1)$

Option D is the correct answer.

Answer 2

Answer:

D.

Step-by-step explanation: