Question

find the distance between x and y with x(2, -9) and y(-10, -1)

Explanation:

Step1: Recall distance formula

The distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

Step2: Identify coordinates

Here, \(x_1 = 2\), \(y_1=-9\), \(x_2=-10\), \(y_2 = - 1\).

Step3: Substitute into formula

Calculate \(x_2 - x_1=-10 - 2=-12\) and \(y_2 - y_1=-1-(-9)=8\).
Then \(d=\sqrt{(-12)^2 + 8^2}=\sqrt{144 + 64}=\sqrt{208}\).

Step4: Simplify \(\sqrt{208}\)

\(\sqrt{208}=\sqrt{16\times13}=4\sqrt{13}\approx14.42\) (if decimal is needed). But exact form is \(4\sqrt{13}\), or simplified radical. Wait, wait, let's recalculate: \((-12)^2 = 144\), \(8^2=64\), \(144 + 64 = 208\). \(\sqrt{208}=\sqrt{16\times13}=4\sqrt{13}\approx14.42\). Wait, but maybe I misread the coordinates. Wait the problem says \(X(2,-9)\) and \(Y(-10, - 1)\)? Let me check again. So \(x_1 = 2\), \(x_2=-10\), so difference is \(-12\), squared is 144. \(y_1=-9\), \(y_2=-1\), difference is \(8\), squared is 64. Sum is 208. Square root of 208: 208 divided by 16 is 13, so \(4\sqrt{13}\approx14.42\).

Answer:

The distance between \(X\) and \(Y\) is \(4\sqrt{13}\) (or approximately \(14.42\)).