Question

how much longer is line segment ab than line segment bc? (17, 28) (-1, 4) (-21, -17) 7 units 1 unit 0 units 2 units

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: Calculate length of AB

Let $A=(17,28)$ and $B=(- 1,4)$. Then $x_1 = 17,y_1 = 28,x_2=-1,y_2 = 4$.
$AB=\sqrt{(-1 - 17)^2+(4 - 28)^2}=\sqrt{(-18)^2+(-24)^2}=\sqrt{324 + 576}=\sqrt{900}=30$.

Step3: Calculate length of BC

Let $B=(-1,4)$ and $C=(-21,-17)$. Then $x_1=-1,y_1 = 4,x_2=-21,y_2=-17$.
$BC=\sqrt{(-21+1)^2+(-17 - 4)^2}=\sqrt{(-20)^2+(-21)^2}=\sqrt{400+441}=\sqrt{841}=29$.

Step4: Find the difference

$AB - BC=30 - 29=1$.

Answer:

1 unit