Question

In the diagram, the coordinates of endpoints A and B are (-3, 9) and (9, 5). What are the coordinates of point H?

Answer 1

A. (-1.5, 8.5)
B. (0, 8)
C. (1.5, 7.5)
D. (6, 6)
E. (7.5, 5.5)

Answer 2

I was thinking D or E

Answer 3

what is the distance between points A and C

Answer 4

@mathmath333 how will I figure that out

Answer 5

without the information it will be difficult to find the co-ordinates of point H

Answer 6

theres a picture but no other info

Answer 7

the pic is ^^^^^

Answer 8

@ganeshie8 help please

Answer 9

the distance between each point is equal so we have to find the distannce between each piont

Answer 10

\(8m=\sqrt{(-3-9)^2+(9-5)^2}\\
=4\sqrt{10}\\
m=\dfrac{\sqrt{10}}{2}\)

Answer 11

m=1.5

Answer 12

now let the co-ordinates of point H
be \((x,y)\)
distane between point H and B is
thus
\(\sqrt{(x-9)^2+(y-5)^2}=2\times \dfrac{\sqrt{10}}{2}\\
(x-9)^2+(y-5)^2=10\\
\)

Answer 13

so 7.5 ?

Answer 14

similarly the distance between H and A is

thus \(\sqrt{(x-(-3))^2+(y-9)^2}=6\times \dfrac{\sqrt{10}}{2}\\
(x+3)^2+(y-9)^2=90\\
\)

Answer 15

so now u have solve for \((x,y)\) which are the co-ordinates of point H

Answer 16

u have 2 equations

Answer 17

how would i set that up though? im sorry i just really don't get these kinda questions

Answer 18

solve any one equation in terms of \(x\) or \(y\) and put its value in the other equation

Answer 19

there might be a shorter way but i m unaware of that

Answer 20

http://www.wolframalpha.com/input/?i=%28x-9%29%5E2%2B%28y-5%29%5E2%3D10%2C%28x%2B3%29%5E2%2B%28y-9%29%5E2%3D90