Question

1.04: swbat determine the length of a segment using the distance formula. directions: complete the following questions by showing all work and annotations. keep work organized and box any final answer. all work must be shown in order to receive full credit. #1.) ab with endpoints a(4,12) and b(0,20) is cut into 4 equal pieces. what is the length of one of these pieces? a) √80 b) 4√5 c) 16√5 d) √5 **#2.) consider the following: the length of cd is 7. which of the following segments below is larger than cd? i: ab with endpoints a(4, -1) and b(-1, -5) ii: segment ef where e is (2,0) and f is (4, -7) a) i only b) ii only c) i and ii d) neither

Explanation:

Step1: Find length of AB using 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 $A(4,12)$ and $B(0,20)$, we have $x_1 = 4,y_1=12,x_2 = 0,y_2 = 20$. Then $d_{AB}=\sqrt{(0 - 4)^2+(20 - 12)^2}=\sqrt{(-4)^2+8^2}=\sqrt{16 + 64}=\sqrt{80}=4\sqrt{5}$. Since AB is cut into 4 equal - pieces, the length of one piece is $\frac{4\sqrt{5}}{4}=\sqrt{5}$.

Step2: Find length of AB for second - part

For points $A(4,-1)$ and $B(-1,-5)$, using the distance formula $d_{AB}=\sqrt{(-1 - 4)^2+(-5+1)^2}=\sqrt{(-5)^2+(-4)^2}=\sqrt{25 + 16}=\sqrt{41}\approx6.4$.

Step3: Find length of EF

For points $E(2,0)$ and $F(4,-7)$, using the distance formula $d_{EF}=\sqrt{(4 - 2)^2+(-7 - 0)^2}=\sqrt{2^2+(-7)^2}=\sqrt{4 + 49}=\sqrt{53}\approx7.3$.

Answer:

1. d) $\sqrt{5}$
2. c) I and II