SOLUTION: Given (11, 7) and (x, −5), find all x such that the distance between these two points is 13. Separate multiple answers with a comma. x =

Algebra ->  Coordinate-system -> SOLUTION: Given (11, 7) and (x, −5), find all x such that the distance between these two points is 13. Separate multiple answers with a comma. x =      Log On


   

Question 1186672: Given (11, 7) and (x, −5), find all x such that the distance between these two points is 13. Separate multiple answers with a comma.
x =
Found 3 solutions by greenestamps, ikleyn, Edwin McCravy:
Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


Use the distance formula -- aka the Pythagorean Theorem....

%2811-x%29%5E2%2B%287-%28-5%29%29%5E2=13%5E2
%2811-x%29%5E2%2B144=169
%2811-x%29%5E2=25
11-x=5 or 11-x=-5
x=6 or x=16

ANSWERS: 6, 16

The problem can be solved without formal algebra.

A quick sketch of the problem shows a right triangle with hypotenuse 13 and one leg 12; that means the other leg must have length 5. So the two values of x that satisfy the conditions of the problem are 11-5=6 and 11+5=16.

Answer by ikleyn(52750) About Me  (Show Source):
You can put this solution on YOUR website!
.

The distance equation is

    sqrt%28%281-x%29%5E2+%2B+%287-%28-5%29%29%5E2%29 = 13.


Square both sides

    %2811-x%29%5E2 + 12%5E2 = 13%5E2

    %2811-x%29%5E2 = 169 - 144 = 25

    11 - x = +/- 5


    a)  11 - x = 5   --->  11 - 5 = x  --->  x = 6.

    b)  11 - x = -5  --->  11 + 5 = x  --->  x = 16.


ANSWER.  x = 6  or  x = 16.

Solved.



Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

We plot the point (11,7) and draw the horizontal line y = -5, 
all of whose points are (x, -5) for different values of x.  Then we take a
compass, open it up to 13 units, and with the sharp point on (11,7), we swing an
arc that cuts the horizontal line in two places:



Then we draw radii (in green) from (11,7) to those two points. 



Next we draw a perpendicular (in blue) from (11,7) to the horizontal line, to
split the isosceles triangle formed into two congruent right triangles.
It goes from (11,6) down to the point (11,-5):



We count the units on the graph paper and find that the blue leg of each right
triangle is 12 units long.
We calculate the length of the bottom legs of each right triangle, using
the Pythagorean theorem:











So the point where the green lines cut the horizontal line are
the two points which are 5 points left and right of (11,-5),
which are (6,-5), and (16,-5),

So the two values of x are 6 and 16.

Edwin