+7 There are four points that are 5 units from the line y=13 and 13 units from the point (7,13). What is the sum of the x and y and coordinates of all four of these points?
+128406 Not as difficult as it seems once we draw a graph : https://www.desmos.com/calculator/wars2lfhv7
Construct a circle with a center of (7,13) and a radius of 13
And consider the line y = 13
This line will pass through (7,13)
The equation of our circle is
(x-7)^2 + ( y - 13)^2 = 169
Let y = 18 ( this will be 5 vertical units from y = 13 )
(x - 7)^2 + (18 - 13)^2 = 169
(x - 7)^2 + 5^2 = 169
(x - 7)^2 + 25 = 169
(x - 7)^2 = 169 -25
(x -7)^2 = 144
12^2 = 144 and (-12)^2 = 144
So x must be 19 or x = -5
And one of the points we need is ( 19, 18)This point will lie on our circle and will be 13 units from (7 ,13) and it will be 5 units from the line y = 13
And one ot the other points we need is (-5, 18)
And using symmetry.....the other two points we need are (19, 13 - 5) = (19, 8) and (-5,13-5) = (-5,8)
