Find the area of a trapezoid with sides of 8cm 14cm 8cm 21cm and a height of 7cm

Write the equation of the perpendicular bisector of . Point B is located at (–3, 1), and point C is located at (1, 5).

maxonik [38]

The equation of perpendicular bisector of BC is

$y=-x+2$

Further explanation:

A perpendicular bisector passes through the mid-point of a line so to get an ordered pair from which the perpendicular bisector will pass we need to find the mid-point of BC.

$Mid-point = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )\\Here\\(x_1,y_1) = (-3,1)\\(x_2,y_2) = (1,5)\\Putting\ values\ in\ formula\\M = (\frac{-3+1}{2} , \frac{1+5}{2} )\\= (\frac{-2}{2} ,\frac{6}{2})\\= (-1, 3)$

So the perpendicular bisector will pass through (-1,3)

Let m1 be the slope of BC

Then

$m_1 = \frac{y_2-y_1}{x_2-x_1} \\=\frac{5-1}{1+3} \\=\frac{4}{4}\\ =1$

Let m2 be the slope of perpendicular bisector

We know that the product of slopes of perpendicular lines is -1.

$m_1.m_2 = -1\\1*m_2 = -1\\m_2 = -1$

The standard form of point-slope form of line is:

$y=mx+b$

Putting the value of slope of bisector we get

$y=(-1)(x)+b\\y=-x+b$

To find the value of b, put the ordered pair (-1,3) in the equation

$3 = -(-1) +b\\3= 1+b\\3-1 =b\\b=2\\$

Putting the values of m and b in standard form

$y=-x+2$

Hence the equation of perpendicular bisector of BC is

$y=-x+2$

Keywords: Perpendicular bisector, Point-slope form

Learn more about point-slope form at:

#LearnwithBrainly

6 0

3 years ago

A cake is cut into 8 slices. If i give 3 slices away,what fraction of cake is left

Georgia [21]

Answer: 5/8

Step-by-step explanation: Its cut into 8 slices and you give 3 away so you do 8-3=5 and that means it would be 5/8.

3 0

3 years ago

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15. The temperature C, in degrees, that is equivalent to a temperature of F degrees Fahrenheit is given by graph of this equatio

7nadin3 [17]

Answer:

A. How can the equation be used in temperature conversion?

You take the conversion equation C = (5/9) (F - 32) and you replace the F by the value of Fahrenheit degrees... then solve the calculations to get the degrees in Celsius.

For example, if you have 80°F to convert in °C:

C = (5/9) (80 - 32) = (5/9) (48) = 26.66 °C

B. How can you use the graph to find the body temp in C?

Using the graph will give a very imprecise measure due the scale of the graph.

But you would have to find 98.6 on the axis of X (it represents the °F), then go upwards until you find the line....

Then report that position on the line on the Y-axis (representing the °C) to get your measure.

7 0

3 years ago

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Which expressions are equivalent to cos2(105°) – sin2(105°)? Check all that apply.

IgorLugansk [536]

Answer:

1,2,5

Step-by-step explanation:

Failed on EDG

4 0

3 years ago

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Factor 21x^3 y^2 – 3x^2y + 75x^4

malfutka [58]

The greatest common factor is 3x². The rest doesn't factor.
21x³y² -3x²y +75x⁴ = 3x²(7xy² -y +25x²)

6 0

3 years ago

Find the area of a trapezoid with sides of 8cm 14cm 8cm 21cm and a height of 7cm​

Find the area of a trapezoid with sides of 8cm 14cm 8cm 21cm and a height of 7cm