Question

1. find st if s(-3, 10) and t(-2, 3).

Explanation:

Step1: Recall the distance formula

The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(S(-3,10)\) means \(x_1=-3,y_1 = 10\) and \(T(-2,3)\) means \(x_2=-2,y_2=3\).

Step2: Substitute the values into the formula

First, calculate \(x_2 - x_1=-2-(-3)=-2 + 3=1\) and \(y_2 - y_1=3 - 10=-7\). Then, substitute these into the distance formula: \(ST=\sqrt{(1)^2+(-7)^2}\).

Step3: Simplify the expression

Calculate the squares: \(1^2 = 1\) and \((-7)^2=49\). Then add them: \(1 + 49=50\). So, \(ST=\sqrt{50}\). Simplify \(\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}\approx7.07\) (if we want the decimal approximation) or we can leave it as \(5\sqrt{2}\).

Answer:

The length of \(ST\) is \(5\sqrt{2}\) (or approximately \(7.07\)).