Jamal needs several feet of wood for a birdhouse

Find an equation for the perpendicular bisector of the line segment whose endpoints are

Andrew [12]

The equation of the perpendicular bisector is y = $-\frac{7}{2}$ x + 2

Step-by-step explanation:

Let us revise the relation between the slopes of perpendicular lines

The product of the slopes of two perpendicular lines is -1
That means if the slope of one of them is m, then the slope of the other is $-\frac{1}{m}$
You reciprocal the slope of one and change its sign to find the slope of the other

The mid point of a segment whose endpoints are $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

The perpendicular bisector of a line is the line that intersect it in its mid-point and formed 4 right angles

∵ The end point of a given line are (9 , -3) and (-5 , -7)

∴ $x_{1}=9$ and $x_{2}=-5$

∴ $y_{1}=-3$ and $y_{2}=-7$

- Find the slope of the line by using the rule of the slope $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

∵ $m=\frac{-7-(-3)}{-5-9}=\frac{-7+3}{-14}=\frac{-4}{-14}=\frac{2}{7}$

∴ The slope of the given line is $\frac{2}{7}$

To find the slope of the perpendicular bisector of it reciprocal it and change its sign

∴ The slope of the perpendicular bisector = $-\frac{7}{2}$

∵ The form of the linear equation is y = mx + b, where m is the

slope and b is the y-intercept

- Substitute the value of m in the equation

∴ The equation of the perpendicular bisector is y = $-\frac{7}{2}$ x + b

To find b substitute x and y in the equation by a point on the line

∵ The perpendicular bisector of the given line intersect it at

its midpoint

- Find the mid-point of the given line busing the rule above

∵ $x_{1}=9$ and $x_{2}=-5$

∵ $y_{1}=-3$ and $y_{2}=-7$

∴ The mid-point of the given line = $(\frac{9+(-5)}{2},\frac{-3+(-7)}{2})=(\frac{4}{2},\frac{-10}{2})=(2,-5)$

Point (2 , -5) is also lies on the perpendicular line

∴ x = 2 and y = -5

- Substitute them in the equation

∵ -5 = $-\frac{7}{2}$ (2) + b

∴ -5 = -7 + b

- Add 7 to both sides

∴ 2 = b

- Substitute the value of b in the equation

∴ The equation of the perpendicular bisector is y = $-\frac{7}{2}$ x + 2

The equation of the perpendicular bisector is y = $-\frac{7}{2}$ x + 2

Learn more:

You can learn more about the linear equation in brainly.com/question/11223427

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8 0

3 years ago

A simple random sample of 144 observations was taken from a large population. The sample mean and the standard deviation were de

Vera_Pavlovna [14]

Answer:

The standard error of mean = 10

Step-by-step explanation:

Given a simple sample of 144 observations was taken from a large population.

The size of large sample 'n' = 144

Given sample mean and the standard deviation were determined to be 1234 and 120 respectively.

Given standard deviation of sample (S) = 120

The standard error of mean is determined by

$SE (X^{-} ) = \frac{S.D}{\sqrt{n} }$

$SE (X^{-} ) = \frac{120}{\sqrt{144} } = 10$

Final answer:-

The standard error of mean = 10

4 0

3 years ago

The following situation can be modeled by a linear function. Write an equation for the linear function and use it to answer the

Alenkinab [10]

Answer:

The function is y = 17000 + 820 x

where: y = price of the car.

x = time in years.

After 3.3 years, the car will cost $19706.

Step-by-step explanation:

Hi there!

Let y be the price of the car.

After the first year, the price of the car will be:

y = 17000 + 820

After the second year:

y = 17000 + 820 + 820 or 17000 + 820(2)

After the third year:

y = 17000 + 820 + 820 + 820 or 17000 + 820(3)

Then, after x years:

y = 17000 + 820 x

After 3.3 year, the car will cost:

y = 17000 + 820(3.3) = 19706

After 3.3 years, the car will cost $19706.

6 0

4 years ago

What is the area of the trapezoid?

disa [49]

Answer:

The area is 100 meters squared

Step-by-step explanation:

8 0

4 years ago

Work out the value of angle x. and give a reason for your answer. pls help!

Stella [2.4K]

Answer:

60°

Step-by-step explanation:

Since, all sides of the given triangle are marked with identical signs.

So, measures of all sides are equal.

Therefore, it is an equilateral triangle.

Measure of each angle of an equilateral triangle is 60°.

So, x = 60° ( Alternate angles)

5 0

3 years ago