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# Coordinates

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There are four points that are 5 units from the line y=13 and 18 units from the point (7,15). What is the sum of the x and y and coordinates of all four of these points?

Jul 26, 2021

#1
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There are four points that are 5 units from the line y=13 and 18 units from the point (7,15). What is the sum of the x and y and coordinates of all four of these points?

Hello Guest!

$$\sqrt{18^2-(x-7)^2}+15=13+5\ |-18\\ \sqrt{18^2-(x-7)^2}-3=0$$

$$x_1=7-3\sqrt{35}\\ \color{blue}x_1=-10.748\\ \color{blue}y_1=18\\ x_2=7+3\sqrt{35}\\ \color{blue}x_2=24.748\\ \color{blue}y_2=18$$

$$-\sqrt{18^2-(x-7)^2}+15=13-5\ |-8\\ -\sqrt{18^2-(x-7)^2}+7=0$$

$$\color{blue}y_3=8\\ x_3=7-5\sqrt{11}\\ \color{blue}x_3=-9.583\\ \color{blue}y_4=8\\ x_4=7+5\sqrt{11}\\ \color{blue}x_4=23.583\\$$

$$P1\ [-10.748, 18]$$        $$P2\ [24.748, 18]$$

$$P3\ [-9.583, 8]$$            $$P4\ [23.583,8]$$ !

Jul 26, 2021
edited by asinus  Jul 26, 2021
edited by asinus  Jul 26, 2021
edited by asinus  Jul 27, 2021
edited by asinus  Jul 27, 2021