help with distance formula?

Question

(4b, b) , (3b, 0)

i know how the plug the "x's" and "y's" into the distance formula, but how do you solve it? when you don't know what b is equal to? please explain. thanks for your help.

Answer 1

When you don't know what b is equal to, and the question asks for you to solve for b, then you do just that: put the equation in the term of b = equation.
distance ^2 =[(x^2-x1)^2 + (y2-y1)^2]
distance^2 = (3b-4b)^2 + (0-b)^2
d^2 = b^2 + b^2
d^2 = 2b^2
(d^2)/2 = b^2
d/root2 = b (be sure to get the square root of 2 out of the denominator)
b = root 2 * d/2

otherwise, if your teacher wants you to keep it in terms of the distance, then your answer is the following, keeping it in terms of b:

d = (root 2) * b

Either way, you can simplify an equation with two variables. It's helpful for down the line when math gets more complicated. Hope this helps!

Answer 2

Here b is a variable, meaning that we don't really know what it is. Since the question does not ask us to find out what b actually is, we can just solve the equation by looking for a value for d (distance).

Here's the distance formula:
d= sqrt [(x1-x2)^2 + (y1-y2)^2]

If we plug in your coordinates:

d= sqrt [(4b-3b)^2 + (b-0)^2]

Now, simplify:
d= sqrt [b^2 + b^2]
d= sqrt [2b^2]
d= b * sqrt [2]

Answer 3

Your answer would include the variable b in it, without you still knowing what b was.

(4b - 3b)^2 + (b-0)^2 = distance^2
b^2 + b^2 = distance ^2
2*b^2 = distance^2
sqrt(2) * b = distance

Answer 4

You don't have to know what 'b' is equal to. One hundred plus one hundred == two hundred. Two thousand plus three thousand = five thousand. Fifteen google plus 20 google equals 35 google (and you don't have to know what number a google represents). So, one 'b' plus two 'b's equals three 'b's and you don't have to know what a 'b' represents.

[The distance you want is sqrt(2)*b.]