Find the x coordinate (1,5) (X,-5) d=10
Answer (1)
Answer:To get the x-coordinate of the point (X, -5) given that the distance between the points (1, 5) and (X, -5) is 10 units, we can apply the distance formula:Distance Formula: [tex]d =\sqrt (x^{2} -x^{1})^2 + (y^{2} - y^{1})^2\\[/tex]Given:[tex](x^{1}, y^{1}) = (1,5)[/tex][tex](x^{2}, y^{2}) = (X, -5)[/tex][tex]d = 10[/tex]Substitute the values into the distance formula: [tex]10 = \sqrt({X} - 1)^{2} + (-5 -5)^2[/tex]Simplify the equation: [tex]10 = \sqrt(X - 1)^2 + (-10)^2\\10 = \sqrt (X-1)^2 + 100[/tex]Square both sides to eliminate the square root: [tex]100 = (X-1)^2 + 100[/tex]Subtract 100 from both sides: [tex]0 = (X-1)^2[/tex]Take the square root of both sides: [tex]X - 1 = 0[/tex]Solve for [tex]X[/tex]: [tex]X=1[/tex]So, the x-coordinate [tex]X[/tex] is [tex]1[/tex].
