Question

1. given the points below, find xy. round to the nearest hundredth.

x(-9, 2) and y(5, -4)
xy =

Explanation:

Step1: Recall Distance Formula

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\). For points \(X(-9, 2)\) and \(Y(5, -4)\), let \(x_1=-9\), \(y_1 = 2\), \(x_2=5\), \(y_2=-4\).

Step2: Calculate Differences

Find \(x_2 - x_1 = 5 - (-9)=5 + 9 = 14\) and \(y_2 - y_1=-4 - 2=-6\).

Step3: Square the Differences

Square the results: \((14)^2 = 196\) and \((-6)^2 = 36\).

Step4: Sum the Squares

Add the squared values: \(196 + 36 = 232\).

Step5: Take the Square Root

Take the square root of 232: \(\sqrt{232}\approx15.23\) (rounded to the nearest hundredth).

Answer:

\(15.23\)