Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

hmmm

The fixed point C has coordinates (8,-6,5) and the variable point D has coordinates (d,d,2d). Show that (AP)² = 6d² - 24d + 125.

I manage to get the right answer, but I don't really see how it works? anyone mind explaining?

From there I just square both sides, expand and simplfy to get to the answer above.

Thanks.

Last edited by Daniel123 (2007-12-05 10:22:05)

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: hmmm

what do you mean you don't see how it works?

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Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: hmmm

I don't see why that is the distance between the two points.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: hmmm

Let AP_x, AP_y and AP_z denote the distance that A is from P, with respect to the x, y and z directions. Then:

AP_x is d-8
AP_y is d-(-6) = d+6
AP_z is 2d-5

Each time got by taking the first co-ordinate away from the second.
Now you use Pythagoras to find AP, and then expand and simplify as you said.

(To be completely rigorous, use Pythagoras on the first two to find the distance from A to P with respect to the xy plane, and then use that length with AP_z to find AP)

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Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: hmmm

ahh you see I just had trouble visualizing it. I have now drawn out a diagram, using a cuboid with the two points at the near top left and far bottom right corners, and used Pythagoras twice as you said to find the distance. thanks.