Question

find the distance between the pair of points.
e(11, -1), f(-1,8)
d = \boxed{} (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall 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, \(x_1 = 11,y_1=-1,x_2=-1,y_2 = 8\).

Step2: Substitute values into formula

Substitute \(x_1 = 11,y_1=-1,x_2=-1,y_2 = 8\) into the formula:

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Wait, wait, let's recalculate the differences. Wait, \(x_2 - x_1=-1-11=-12\), \(y_2 - y_1 = 8 - (-1)=9\). Then \((-12)^2 = 144\), \(9^2=81\), sum is \(144 + 81=225\), square root of 225 is 15. Wait, but let's check again. Wait, the distance formula is \(\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), so that's correct. Wait, but maybe I made a mistake in signs? Let's check: \(x_1 = 11\), \(x_2=-1\), so \(x_2 - x_1=-1 - 11=-12\), squared is 144. \(y_1=-1\), \(y_2 = 8\), so \(y_2 - y_1=8 - (-1)=9\), squared is 81. Sum is 225, square root is 15. So the distance is 15.

Answer:

\(15\)