Mathematics, 28.08.2019 16:10, ExclusiveNay

Given three points a(-1,-2) b(3,4) c(3,6). find the perpendicular bisector of
a) ab
b)bc

Answers: 2

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Answers

The perpendicular bisector is line that divides another line into two equal parts, and is also at right angles to the line it is bisecting.

Question A) We need to work out the following: Midpoints of AB (since it's a bisector) Perpendicular gradient of AB (since its the perpendicular bisector) Finally, equation of perpendicular gradient, through the midpoint of AB (since the bisector is halfway through AB)

Working out the Midpoint of AB:

To work out the midpoint, you take the average (add and divide by 2) of the x coordinates and the y coordinates for points A and B:

xcoords of Midpoint = $\frac{-1+3}{2}}=1$

ycoords of Midpoint = $\frac{-2+4}{2} =1$

So the coordinates of the Midpoint is: (1, 1)

Working out perpendicular gradient:

First, we work out the gradient of AB. Then to get the perpendicular gradient, we take the negative reciprocal of that gradient (by flipping the fraction and putting a negative sign in front).

$Gradient =\frac{y1-y2}{x1-x2}=\frac{-2-4}{-1-3}=\frac{-6}{-4}=\frac{3}{2}$

So perpendicular gradient = negative reciprocal of $\frac{3}{2}$ = $-\frac{2}{3}$

Equation of Perpendicular gradient through Midpoint

To get the equation, we can use the following formula:

y-y1=m(x-x1)

Where:

y1 = y coordinate of the midpoint we worked out (1 )x1 = x coordinate of the midpoint we worked out (1 )m = perpendicular gradient we worked out (-2/3)

So all we do now is substitute in the values into the equation and rearrange for y:

y -y1=m(x-x1)

$y-1=-\frac{2}{3} (x-1)$ (times both sides by 3)

3y-3=-2(x-1) (expand brackets)

3y -3=-2x+2

3y=-2x +5

$y=-\frac{2}{3}x+\frac{5}{3}$

Perpendicular Bisector of AB is: $y=-\frac{2}{3}x+\frac{5}{3}$

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Question B)

We just follow the same steps as for Question A, except we use the coordinates for B and C, instead of A and B, so I will include less explanation for this question.

$Midpoint=(\frac{x1+x2}{2},\frac{y1+y2}{2})=(\frac{3+3}{2},\frac{4+6}{2})=(3, 5)$

Gradient:

Notice, the x coordinates for B(3, 4) and C (3, 6) are the same. That means the gradient is 0, and so is the perpendicular gradient. So we can skip straight to get the equation of perpendicular bisector.

Equation of perpendicular bisector:

y-y1=m(x-x1)

y-5=0(x-3)

y-5 = 0

y=5

The perpendicular bisector of BC is: y=5

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Answers:

a) $y=-\frac{2}{3}x+\frac{5}{3}$

b) y=5

answered: Guest

2. 2 3/5.

3. 2 1/2.

step-by-step explanation:

6 - 3 2/5

= 6 - 17/5

= 30/5 - 17/5

= 13/5

= 2 3/5 (answer).

5 1/4 - 2 3/4

= 21/4 - 11/4

= 10/4

= 2 1/2 (answer).

With alll of except for the 2 that i did already

answered: Guest

1. sometimes

2. never

3 .08c = 7.50+.05c 250 pages

step-by-step explanation:

1. sometimes

the theoretical probability of rolling a 1 is 1/6. perhaps you got really lucky and never rolled a 1 in those 60 times. your experimental probability is 0. or perhaps you rolled a 1 20 times. your experimental probability is 20/60 is 1/3. it really just depends on how you rolled in that experiment.

2. never

the probability of the event occurring is 1. that is being 100 % sure it will happen. that is the maximum amount of confidence we have.

3. no customer card cost: .08 times number of pages

customer card cost: 7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03