Question

Help on 4 multiple choice questions please

Answer 1

1. A line segment on a number line has its endpoints at -9 and 6. Find the coordinate of the midpoint of the segment.
1.5
-1.5
2
-3

2. Find the coordinates of the midpoint HX given that H(-1,3) and X(7, -1).
(3, 1)
(0, 4)
(-3, 1)
(-4, 0)

3. Find the distance between the points R(0,5) and S(12,3). Round the answer to the nearest tenth. 10.4 16 12.2 11.8 4. An airplane T(80, 20) needs to fly to both U(20,60) and V(110,85). What is the shortest possible distance for the trip?
165 units
170 units
97 units
169 units

Answer 2

4. An airplane T(80, 20) needs to fly to both U(20,60) and V(110,85). What is the shortest possible distance for the trip?
165 units
170 units
97 units
169 units

Answer 3

for number 3 i put the wrong choices, they are
A. 10.4
B. 16
c. 12.2
d. 11.8

Answer 4

@johnweldon1993

Answer 5

Midpoint would be

\[\large \frac{x_1 + x_2}{2}\] so \[\large \frac{-9 + 6}{2} = ?\]

Answer 6

Same for the second except now we have both the 'x' and the 'y'

\[\large Midpoint = (\frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2})\]

Answer 7

- 3/2?

Answer 8

Right, simplify that a bit more...what is -3 / 2 ?

Answer 9

Now and for the third one, the distance formula is

\[\large d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]

Answer 10

nevermind thats complicated:(

Answer 11

thanks though:(

Answer 12

Tell me what you're stuck on :)

Answer 13

I just dont understand math.. period.:(

Answer 14

Well lets do it slow.. :)

Number 1

Answer 15

on a number line that goes from -9 to +6 ...we want what is exactly in the middle

Answer 16

its -1.5!:)

Answer 17

correct?:(

Answer 18

How we do that...is by finding the midpoint.

We add the 2 numbers and then divide that result by 2. Why? because it gives the average (middle) of the two.

So

\[\large \frac{x_1 + x_2}{2}\]
We plug in -9 for x_1 and 6 for x_2

\[\large \frac{-9 + 6}{2} = \frac{-3}{2} = -1.5\]

Answer 19

So yes, correct :)

Answer 20

awesome!

Answer 21

Alright number 2...Same thing we just did but this time it will look like:

this

Answer 22

WOW!?

Answer 23

We want whatever is in the middle there...

so again we do the midpoint thing... lets focus on the 'x' midpoint first (because as you see the points look like (x , y)

so for the 'x'

\[\large Midpoint_x = \frac{-1 + 7}{2} = \frac{6}{2} = 3\]

Answer 24

(3,1)

Answer 25

Does that graph look too weird for you? :)

But yes that is correct

Answer 26

YAY!:) and same for 3?

Answer 27

12.2 for #3 right

Answer 28

Indeed^ :)

Answer 29

yay! i just make problems harder then what they really are. now #4 looks hard?:?

Answer 30

Okay then we'll walk through it hun :)

So its the same thing we just did for number 3...but adding in 2 distances...

so firstly...we want to know which will be quicker Going from:

T to U to V

Or

T to V to U?

Answer 31

And how we figure that out...is

find the distance from T to U first...

Answer 32

ok so 70,50?

Answer 33

idk

Answer 34

Not quite remember that formula we did before?

\[\large \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]

so knowing that T = (x1 , y1) = (80 , 20)

and U = (x2 , y2) = (20 , 60)

Answer 35

okay

Answer 36

So after plugging in ALL those points and simplifying we get...?

Answer 37

165 units?

Answer 38

\[\large \sqrt{(20 - 80)^2 + (60 - 20)^2}\]
\[\large \sqrt{(-60)^2 + (40)^2}\]
\[\large \sqrt{(3600) + (1600)}\]
\[\large \sqrt{5200}\]
\[\large \approx 72.111\]

That is the distance from T to U

Now what is the distance from U to V?

Answer 39

97

Answer 40

Since the route T-U-V and T-V-U both use U-V, we know they are equal. So just compare which of T-U or T-V is shorter. one of them is sqrt(5200), and the other is sqrt(5125

Answer 41

Either the plane goes to V first and then to U, or to U then V. The governing distance will be from T to U and T to V - whichever one is shorter will determine the route the plane needs to take.

The distance formula is d = sqrt((x2-1x)^2 + (y2-y1)^2). If we use this on TU and TV, we can find the distance traveled:

dTU = sqrt((x2-1x)^2 + (y2-y1)^2)
dTU = sqrt((80 - 20)^2 + (20 - 60)^2)
dTU = sqrt(60^2 + (-40)^2)
dTU = sqrt(3600 + 1600)
dTU = sqrt(5200)
dTU ~ 72.1

dTV = sqrt((x2-1x)^2 + (y2-y1)^2)
dTV = sqrt((80 - 110)^2 + (20 - 85)^2)
dTV = sqrt((-30)^2 + (-65)^2)
dTV = sqrt(9000 + 4225)
dTV = sqrt(13225)
dTV = 115

Thus, it's shorter for the plane to go to U first, and then to V next.

To complete the question, we need to find the distance from U to V:

dUV = sqrt((x2-1x)^2 + (y2-y1)^2)
dUV = sqrt((20 - 110)^2 + (60 - 85)^2)
dUV = sqrt(90^2 + (-25)^2)
dUV = sqrt(8100 + 625)
dUV = sqrt(8725)
dUV ~ 93.4

Thus, going from T to U to V will be 165.5.