SOLUTION: Missing coordinate A(-3,2) , B(x,3) , c(4,5) if AB=BC , Find the value of x???

Question 885250: Missing coordinate A(-3,2) , B(x,3) , c(4,5) if AB=BC , Find the value of x???
Found 2 solutions by richwmiller, algebrapro18:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
(x,3) is not on the same line as A(-3,2) C(4,5) so we cannot just find the midpoint
The distance (denoted by d) between two points in two dimensions is given by the following formula:

sqrt((4-x)^2 + (5-3)^2)=sqrt((-3-x)^2 + (2-3)^2)
x = 5/7

Answer by algebrapro18(249) (Show Source): You can put this solution on YOUR website!
To find x we need to find the distance between A and B and the distance between B and C. We can then set the two distances equal to each other and solve for x, since AB=BC.

So finding the distance between A and B we get:

That's as simplified as that can get. So now we find the distance between B and C:

So now we can set AB = BC and solve for x.
= square both sides to get rid of the square root
Subtract (x2-8x+20) from both sides
combine like terms
add 10 to both sides
divide both sides by 14
x = 10/14 = 5/7
RELATED QUESTIONS
If abcd is a rectangle. Ab=4(X+3), bc=6-(2+y) dc=12(X-5) and ad=3y . Find the value of X... (answered by Fombitz)
Let a, b, c be the roots of p(x) = x^3 + 7x^2 + 10x - 13 - 5x^3 + 25x^2 + 44x - 15. Find (answered by CPhill)
If AC=62, find the value of x. Then find AB and BC. Picture: shows a line with 3... (answered by venugopalramana)
Find the value of x if A, B, and C are collinear points and B is between A and C.... (answered by jhunjiro)
__ Find the length of AB if AC has... (answered by CubeyThePenguin)
Point B is between A and C on line AC. Find values of x, AB, and BC. AC=38 3/4... (answered by ikleyn)
4. ABCD is a rectangle. Find mB. A. 45� B. 90� C. 100� D. 180� (answered by jsmallt9)
B is between A and C. AB=2x-4 BC=7x+5 AC=82 What is the value of x? (answered by tara0066)
AB = 3x, BC = 4x, and AC = 42. Find the value of x if B is between A and C. * (answered by ikleyn)