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)

Question 1: Option B:

Question 2: Option D:

Solution:

Question 1:

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

Slope of the given line:

m = –3.

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

Slope of perpendicular line =

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

Slope -intercept form using point slope formula,

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 = 3.

Slope of parallel lines are equal.

Slope of parallel line =3

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

Point slope formula:

Option D is the correct answer.

yes

step-by-step explanation:

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²