Question

the distance fc
rections: find the distance between each pai
cal form. use your solutions to navigate through

given:
s(9, 0), t(-5, -7)
and: st

7√5 √346
12√3 √130

Explanation:

Step1: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For points \(S(9,0)\) and \(T(-5,-7)\), we have \(x_1 = 9,y_1 = 0,x_2=- 5,y_2=-7\).

Step2: Substitute the values into the formula

First, calculate the differences in \(x\) and \(y\) coordinates: \(x_2 - x_1=-5 - 9=-14\) and \(y_2 - y_1=-7 - 0=-7\). Then, square these differences: \((-14)^2 = 196\) and \((-7)^2=49\). Add these squared values: \(196 + 49=245\). Now, take the square root: \(\sqrt{245}=\sqrt{49\times5}=7\sqrt{5}\).

Answer:

\(7\sqrt{5}\)