SOLUTION: Give the coordinates of a point on a coordinate grid that is a distance of the square root of 5 from point 1,3. Is there a formula to find the answer and how do you work out this p

Algebra ->  Coordinate-system -> SOLUTION: Give the coordinates of a point on a coordinate grid that is a distance of the square root of 5 from point 1,3. Is there a formula to find the answer and how do you work out this p      Log On


   

Question 8083: Give the coordinates of a point on a coordinate grid that is a distance of the square root of 5 from point 1,3. Is there a formula to find the answer and how do you work out this problem?
Thank you
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
Yes, it is the pythagorean formula.
You are trying to find point (x, 0) where the y coordinate is zero, since it is on the X axis.
Points (1, 3), (1, 0), and (x, 0) form a right triangle. One side of it has length one. Another has length x-1. Sum of their squares should be 5:
1%5E2%2B%28x-1%29%5E2%29+=+5
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=3,x=-1.
  • Graphical form: Equation 1%5E2%2B%28x-1%29%2A%28x-1%29=5 was fully solved.
  • Text form: 1^2+(x-1)*(x-1)=5 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+1%5E2%2B%28x-1%29%2A%28x-1%29=5+%29
    For tutors: simplify_cartoon( 1^2+(x-1)*(x-1)=5 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+1+%29%5Ehighlight_red%28+2+%29%2B%28x-1%29%2A%28x-1%29=5.
Replace constants in factor: highlight_red%28+1+%29,highlight_red%28+2+%29 with highlight_green%28+1+%29
It becomes highlight_green%28+1+%29%2B%28x-1%29%2A%28x-1%29=5.
Look at 1%2Bhighlight_red%28+%28x-1%29+%29%2Ahighlight_red%28+%28x-1%29+%29=5.
Reduce similar several occurrences of highlight_red%28+%28x-1%29+%29 to highlight_green%28+%28x-1%29%5E2+%29
It becomes 1%2Bhighlight_green%28+%28x-1%29%5E2+%29=5.
Look at highlight_red%28+1+%29%2B%28x-1%29%5E2=5.
Moved 1 to the right of expression
It becomes %28x-1%29%5E2%2Bhighlight_green%28+1+%29=5.
Look at %28x-1%29%5E2%2B1=highlight_red%28+5+%29.
Moved these terms to the left highlight_green%28+-5+%29
It becomes %28x-1%29%5E2%2B1-highlight_green%28+5+%29=0.
Look at %28x-1%29%5E2%2Bhighlight_red%28+1+%29-highlight_red%28+5+%29=0.
Added fractions or integers together
It becomes %28x-1%29%5E2%2Bhighlight_green%28+-4+%29=0.
Look at %28x-1%29%5E2%2Bhighlight_red%28+-4+%29=0.
Removed extra sign in front of -4
It becomes %28x-1%29%5E2-highlight_green%28+4+%29=0.
Look at highlight_red%28+%28x-1%29%5E2-4+%29=0.
Equation highlight_red%28+%28x-1%29%5E2-4=0+%29 is a quadratic equation: x^2-2*x-3 =0, and has solutions 3,-1
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=3,x=-1.

Universal Simplifier and Solver


Done!