Question

Geomtry help?

Answer 1

39. A map of a city and suburbs shows an airport located at A(25, 11). An ambulance is on a straight expressway headed from the airport to Grant Hospital at G(1, 1). The ambulance gets a flat tire at the midpoint M of . As a result, the ambulance crew calls for helicopter assistance.
a. What are the coordinates of point M?
b. How far does the helicopter have to fly to get from M to G? Assume all coordinates are in miles.

Answer 2

Ok. do you know the midpoint and the distance formula?

Answer 3

no?

Answer 4

http://www.purplemath.com/modules/midpoint.htm http://www.purplemath.com/modules/distform.htm

Answer 5

That website gives good explanations of both. You should go and check those out and then come back here so I can help if you still need it.

Answer 6

ok can we work on it?

Answer 7

Sure. First lets do the first part. Can you see which of the two formulas we would need there?

Answer 8

midpoint

Answer 9

Right! So I'll set that one up.

Answer 10

\[\frac{ 25+1 }{2 },\frac{ 11+1 }{ 2 }\]

Answer 11

oh got it, whats next?

Answer 12

Well now we have the point where the ambulance stopped. which after simplification is the point (13,6), and we have the point (1,1) and we need to know how far apart they are.

Answer 13

So we use the distance formula. I'll go ahead and set that one up.

Answer 14

\[\sqrt{(13-1)^{2}+(6-1)^{2}}\]

Answer 15

do I put that into my cal?

Answer 16

Yup.

Answer 17

even square root?

Answer 18

is that 13 sub 1 or is it neg?

Answer 19

Yup all of it. You could simplify first if you wanted to though.

Answer 20

so the (13-1)^2 = 144 and the (6-1)^2 =25

Answer 21

ok got it! than do I add 144 + 25?

Answer 22

Yup. Then you take the square root of that and thats the distance from point M to G.

Answer 23

so I do sqare root 169 in my cal?

Answer 24

Yes.

Answer 25

I got 13

Answer 26

I got the same thing. Looks like thats your answer!

Answer 27

for A and B?

Answer 28

Well we found a earlier remember? Its asking for the coordinates of the midpoint in part a. We found that right?

Answer 29

ohh, wait what was a afgain the answer?

Answer 30

Scroll up and take a look. What was the final answer after we used the midpoint formula?

Answer 31

was it the sqare root of 13-1?

Answer 32

No. The midpoint formula doesn't have any square roots.

Answer 33

25+1 / 2 that one right?

Answer 34

Right. But thats only the x component of the answer.

Answer 35

what do u mean?

Answer 36

When we use the midpoint formula we are finding a point in the coordinate plane. Points are always ordered with the x component first and the y second, like this (x,y). So the first part of our answer Is the x component of the point and the second part is the y component.

Answer 37

So, 25+1/2=x and 11+1/2=y