Question

segment ab has point a located at (8, 9). if the distance from a to b is 10 units, which of the following could be used to calculate the coordinates for point b?
10 = \sqrt{(x - 9)^2 + (y - 8)^2}
10 = \sqrt{(x - 8)^2 + (y - 9)^2}
10 = \sqrt{(x + 9)^2 + (y + 8)^2}
10 = \sqrt{(x + 8)^2 + (y + 9)^2}

Explanation:

Step1: Use the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(A(8,9)\) is \((x_1,y_1)\) and \(B(x,y)\) is \((x_2,y_2)\), and \(d = 10\).

Step2: Substitute values into the formula

Substitute \(x_1 = 8\), \(y_1=9\), \(d = 10\) into the formula: \(10=\sqrt{(x - 8)^2+(y - 9)^2}\)

Answer:

\(10=\sqrt{(x - 8)^2+(y - 9)^2}\) (the second option)