Mathematics, 22.11.2019 04:31 pattydixon6

What is the slope of the given line segment?
what is the midpoint of the given line segment?
what is the slope of the perpendicular bisector off the given line segment?
what is the equation, in the slope-interception form, of the perpendicular bisector?

What is the slope of the given line segment? what is the midpoint of the given line segment?

Answers: 1

Show answers

Answers

Answer from: jbcupcake

Part 1) The slope of the given line segment is m=-2

Part 2) The midpoint of the given line segment is (2,-2)

Part 3) The slope of the perpendicular bisector of the given line segment is $m_2=\frac{1}{2}$

Part 4) The equation, in the slope-interception form, of the perpendicular bisector is $y=\frac{1}{2}x-3$

Step-by-step explanation:

Part 1) What is the slope of the given line segment?

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have the points

(4,-6) and (0,2)

substitute in the formula

$m=\frac{2+6}{0-4}$

$m=\frac{8}{-4}=-2$

Part 2) What is the midpoint of the given line segment?

We know that

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have the points

(4,-6) and (0,2)

substitute in the formula

$M(\frac{4+0}{2},\frac{-6+2}{2})$

M(2,-2)

Part 3) What is the slope of the perpendicular bisector of the given line segment?

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

m_1*m_2=-1

we have

m_1=-2 ---> slope of the given line segment

substitute

(-2)*m_2=-1

$m_2=\frac{1}{2}$

Part 4) What is the equation, in the slope-interception form, of the perpendicular bisector?

The equation of the line in slope intercept form is equal to

y=mx+b

we have

$m=\frac{1}{2}$

The perpendicular bisector passes through the midpoint of the given line segment

M(2,-2)

substitute

$-2=\frac{1}{2}(2)+b$

-2=1+b

b=-3

therefore

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

Answer from: Quest

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

Answer from: Quest

Bhfydtcycfdrxtxrgggd

Another question on Mathematics

Mathematics, 21.06.2019 18:00

Ineed to know the answer right now! !

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

Asquare picture with sides of 32 inches is to be mounted on a square mat with sides of 52 inches. find the area of the mat that will remain uncovered by the picture.

Answers: 1

Answer

Mathematics, 21.06.2019 20:10

Which ratios are equivalent to 10: 16? check all that apply. 30 to 48 25: 35 8: 32 5 to 15

Answers: 1

Answer

Mathematics, 21.06.2019 21:30

This is a map of the mars exploration rover opportunity predicted landing site on mars. the scale is 1cm : 9.4km. what are the approximate measures of the actual length and width of the ellipse? i mostly need to know how to set it up : )

Answers: 3

Answer

You know the right answer?

What is the slope of the given line segment?
what is the midpoint of the given line segment?...

Questions