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Gemiola [76]
3 years ago
7

Find an equation of the line that is the perpendicular bisector of the line segment joining the points (6,2) and (18,6)

Mathematics
1 answer:
dexar [7]3 years ago
6 0

Answer:

y= -3x +40

Step-by-step explanation:

Properties of perpendicular bisector:

• perpendicular to the given line

• cuts through the center of the given line

The equation of a line can be written in the form of y=mx +c, where m is the gradient and c is the y -intercept.

Let's find the gradient of the given line first.

\boxed{gradient =  \frac{y1 - y2}{x1 - x2} }

Gradient of given line

=  \frac{6 - 2}{18 - 6}

=  \frac{4}{12}

=  \frac{1}{3}

The product of the gradients of perpendicular lines is -1.

m(⅓)= -1

m= -1(3)

m= -3

Substitute m= -3 into the equation:

y= -3x +c

To find the value of c, substitute a pair of coordinates in which the perpendicular bisector passes through into the equation. Since perpendicular bisectors passes through the center of the segment, we can find the point in which the perpendicular bisector passes through using the mid- point formula.

\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )}

Midpoint

= ( \frac{6 + 18}{2} , \frac{6 + 2}{2} )

= ( \frac{24}{2} , \frac{8}{2} )

= (12,4)

y= -3x +c

when x= 12, y= 4,

4= -3(12) +c

4= -36 +c

c= 4 +36

c= 40

Thus, the equation of the perpendicular bisector is y= -3x +40.

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Korvikt [17]
Answer: (3x + 11y)^2

Demonstration:

The polynomial is a perfect square trinomial, because:

1) √ [9x^2] = 3x

2) √121y^2] = 11y

3) 66xy = 2 *(3x)(11y)

Then it is factored as a square binomial, being the factored expression:

 [ 3x + 11y]^2

Now you can verify working backwar, i.e expanding the parenthesis.

Remember that the expansion of a square binomial is:

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- double product of first term times second term =>2 (3x)(11y) = 66xy
- square of the second term => (11y)^2 = 121y^2

=> [3x + 11y]^2 = 9x^2 + 66xy + 121y^2, which is the original polynomial.

7 0
3 years ago
kissa brought an item at Tsh 250,000/= she sold it by a certain price and got loss of 1/4 of the buying price. find the percenta
eimsori [14]

Answer:

Loss %age = 25%

Step-by-step explanation:

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=> 62,500 /-

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Vera_Pavlovna [14]

Answer:

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Step-by-step explanation:

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6x+3y=15

-----------------

6x+3(3x-5)=15

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This is an inappropriate conclusion because of <u>D. At 10 months</u>, ninety percent of toddlers have not reached the developmental milestones to walk.

<h3>What is an inappropriate conclusion?</h3>

An inappropriate conclusion is one arrived at without a proper research design.  An inappropriate conclusion can also be reached when the interpretation of the research result is not based on the findings.

Our conclusion implies that there is a wrong interpretation of the research findings because of the researcher's bias.

Thus, the research conclusion is <u>inappropriate</u> because of Option D.

Learn more about research conclusions at brainly.com/question/24542637

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2 years ago
A dice shows only the numbers 1, 2, and four 3's. The numbers 4, 5, or 6 do not appear in the dice. The dice is tossed, and the
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Answer:

Step-by-step explanation:

is 34=57/655$9

8 0
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