Find all values of x or y such that the distance between the given points is as indicated?

Question

find all values of x or y such that the distance between the given points is as indicated.
(x,7) and (2,3) is 5
if you can show work too, that would be great.
Thanks

Answer 1

Use the distance formula :

(x - 2)^2 + (7 - 3)^2 = 25
x^2 - 4x + 4 + 16 = 25
x^2 - 4x - 5 = 0
x^2 + x - 5x - 5 = 0
x(x + 1) - 5(x + 1) = 0
(x + 1)(x - 5) = 0
x = -1, 5

Hope this helps.

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Answer 2

Okay, I think there are only 2 values, for x and y respectively;
Here's how I do it:

So, (x,7) comared to (2,3). Plotting that on a simple cartesian plane would, according to you, form a +5 slope so kinda like a hill going up 5 squares for every square in length.

Anyways, the point is leading to this:

If x = x and 2
and y = 7, 3

then slope = 2-x / 3 - 7 = 5

From your question, I deduced that the relationship is linear, so it would fit under this:

y = mx + b (where y = second coordinate, m = your slope 5, x first coordinate and the x itself, and b y intercept, where x is 0 and y a given number)

so lets put together your details now:

3 = 5(2) + b
b = 3 - 10
b = -7 (so the line starts from -7y)

Then to find the original 'x' we do this:

7 = 5x - 7
14 = 5x
x = 14/5
x = 2.8
y is 7 in this case.

To conclude, in order to find 'every' value of x and y u do this. In order to find value of x you have to know the y, or vice versa...

Answer 3

(x-2)^2+(7-3)^2=25
x^2-4x-5=0 x=(4+-sqrt(36))/2
so x )=5 and x= -1