1. The problem is to find the distance between two points using the distance formula. 2. The distance formula between points $A(x_1,y_1)$ and $B(x_2,y_2)$ is $$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$. 3. Problem 1: Find the distance between points $A(1,2)$ and $B(4,6)$. - Calculation: $$d=\sqrt{(4-1)^2+(6-2)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5$$. 4. Problem 2: Find the distance between points $C(-3,-1)$ and $D(1,3)$. - Calculation: $$d=\sqrt{(1-(-3))^2+(3-(-1))^2}=\sqrt{4^2+4^2}=\sqrt{16+16}=\sqrt{32}=4\sqrt{2}$$. 5. Problem 3: Find the distance between points $E(0,0)$ and $F(-5,12)$. - Calculation: $$d=\sqrt{(-5-0)^2+(12-0)^2}=\sqrt{(-5)^2+12^2}=\sqrt{25+144}=\sqrt{169}=13$$. Each problem shows how to apply the distance formula step-by-step to find the distance between two points in a plane.