SOLUTION: the point (2,-5) is a vertex of square one whose sides lies on the line x-2y=7 calculate the area of square

Algebra.Com
Question 1106794: the point (2,-5) is a vertex of square one whose sides lies on the line x-2y=7 calculate the area of square
Answer by ikleyn(52754)   (Show Source): You can put this solution on YOUR website!
.
Notice that the point (2,-5) does not lie on the given line, because


2 - 2*(-5) = 2 + 10 = 12   IS NOT EQUAL  to 7.


Hence, we have the line, given by the equation, and a point outside this line.


Clearly, the measure of the side of the square is equal to the distance from the given point to the given line.


To find this distance, you can use the general formula

d = .     (*)


This formula gives the distance from the point (p,q) in the coordinate plane to the line whose equation is  ax + by + c = 0.


In our case,  d =  =  =  = .


Thus we determined that the square side is  units long.


Then the area of the square is   = 5.

Solved.

--------------
Regarding the formula (*), see the lesson
    - The distance from a point to a straight line in a coordinate plane
in this site.


RELATED QUESTIONS

a diagonal of a square lies on the line 3x-5y=14. one vertex is at (0,4). Find an... (answered by Alan3354)
The point (5, 7) lies on the line -2x + 8y = 46. Determine if this point is a solution of (answered by robertb)
Point(a,-2) lies on the line whose equation is 2x-6y=14. What is the value of... (answered by Alan3354)
How many square whose area is 9cm square are needed to cover a region of a big square... (answered by Cromlix)
What is the area of a square whose sides are 5 feet 9 inches long? (answered by Gogonati)
What is the area of square whose sides are... (answered by Fombitz)
In a coordinate system Tom drew a square. One of its diagonals lies on the x-axis. The... (answered by Boreal)
I have a square, divided up into 4 quadrants and need to know which quadrant a point lies (answered by Edwin McCravy)
The point (2,1) lies on the line whose equation... (answered by ikleyn)