Question

main ideas/questions notes distance formula used to find the distance between two points (x1, y1) and (x2, y2) formula: examples 1. find the distance between the two points on the graph. 2. find ab given a-4, 1 and b3, -1. 3. find ef given e-7, -2 and f11, 3

Explanation:

Step1: Recall distance formula

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

Step2: Solve example 2

For points $A(-4,1)$ and $B(3,-1)$, let $(x_1,y_1)=(-4,1)$ and $(x_2,y_2)=(3,-1)$. Then $d_{AB}=\sqrt{(3 - (-4))^2+((-1)-1)^2}=\sqrt{(3 + 4)^2+(-2)^2}=\sqrt{49 + 4}=\sqrt{53}$.

Step3: Solve example 3

For points $E(-7,-2)$ and $F(11,3)$, let $(x_1,y_1)=(-7,-2)$ and $(x_2,y_2)=(11,3)$. Then $d_{EF}=\sqrt{(11-(-7))^2+(3 - (-2))^2}=\sqrt{(11 + 7)^2+(3 + 2)^2}=\sqrt{18^2+5^2}=\sqrt{324+25}=\sqrt{349}$.

Answer:

Example 2: $\sqrt{53}$
Example 3: $\sqrt{349}$