Finding x-, y-values giving listed distances between points

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1) Find x so that the distance between the following points is 13: (-8, 0) and (x, 5)

The solutions which I came up with are 20 and -4. Is that correct?

I didn't understand how to do these:

2) Find y so that the distance between the points is 17: (-8, 4) and (7, y)

3) Find an equation that relates x and y so that (x, y) is equidistant from the two given points: (3, 5/2) and (-7, 1)

Thanks !
 
1) How did you obtain your answer? (Please show your work, so we can try to find the error. You're close, but....)

2) This one works just like (1), except for you're looking for the y-value instead of the x-value. The set-up and solution method are exactly the same. Where are you stuck?

3) Plug (x, y) and (3, 5/2) into the Distance Formula (or, for simplicity's sake, the square of the Distance Formula). Plug (x, y) and (-7, 1) into the Formula in the same way. Since the distances are supposed to be the same, set your two expressions equal. Simplify.

If you get stuck, please reply showing all of the steps you have tried. Thank you.

Eliz.
 
this is my work for the first one, finding x:

findingx.jpg
 
FYI: You don't "have" to use images. Typing is just fine:

. . . . .Your work:

. . . . .D = sqrt[(x_2 - x_1)^2 + (y_2 - y_1)^2]

. . . . .13^2 = (sqrt[(-8 - x)^2 + (0 - 5)^2])^2

. . . . .169 = 25 + 64 - 16x + x^2

. . . . .0 = x^2 - 16x - 80

. . . . .(x - 20)(x + 4) = 0

. . . . .x = 20 or x = -4

For myself, I would probably have shown more steps in the middle:

. . . . .Alternate work:

. . . . .13^2 = (sqrt[(-8 - x)^2 + (0 - 5)^2])^2

. . . . .Note: (-8 - x)^2 = (-1)^2 (8 + x)^2 = (x + 8)^2

. . . . .169 = (sqrt[x^2 + 16x + 64 + 25])^2

. . . . .169 = x^2 + 16x + 89

. . . . .0 = x^2 + 16x - 80

. . . . .0 = (x + 20)(x - 4)

. . . . .x = -20 or x = 4

Checking:

. . . . .sqrt[(-8 + 20)^2 + (0 - 5)^2]

. . . . .= sqrt[(-12)^2 + 25]

. . . . .= sqrt[114 + 25]

. . . . .= sqrt[169]

. . . . .= 13

So x = -20 "checks". (Note: x = +20, x = -4 do not check.)

Eliz.
 
I still don't understand how to do the 3rd one. When the teacher briefly showed us in class, I remember that she started off by somehow using the midpoint formula for it.
 
amandamandy said:
...the 3rd one....somehow using the midpoint formula for it.
Click to expand...
The Midpoint Formula would give you exactly one point equidistant from the two listed points. You need to find a formula for all points equidistant. To do this, try following the steps outlined in the first reply.

Eliz.
 
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