Question

question 5 of 10 determine which set(s) of coordinates below are colinear. set 1: a(0, - 3), b(2, - 6) and c(4, - 9) set 2: d(0,14), e(1, - 7) and f(2,0) set 3: g(0,5), h(2,0) and i(4, - 5)

Explanation:

Step1: Recall slope - formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. If three points are collinear, the slope between any two pairs of points is the same.

Step2: Calculate slope for Set 1

For points $A(0,-3)$ and $B(2,-6)$:
$m_{AB}=\frac{-6-(-3)}{2 - 0}=\frac{-6 + 3}{2}=\frac{-3}{2}$
For points $B(2,-6)$ and $C(4,-9)$:
$m_{BC}=\frac{-9-(-6)}{4 - 2}=\frac{-9 + 6}{2}=\frac{-3}{2}$
Since $m_{AB}=m_{BC}$, points $A$, $B$, and $C$ are collinear.

Step3: Calculate slope for Set 2

For points $D(0,14)$ and $E(1,-7)$:
$m_{DE}=\frac{-7 - 14}{1-0}=\frac{-21}{1}=-21$
For points $E(1,-7)$ and $F(2,0)$:
$m_{EF}=\frac{0-(-7)}{2 - 1}=\frac{7}{1}=7$
Since $m_{DE}
eq m_{EF}$, points $D$, $E$, and $F$ are not collinear.

Step4: Calculate slope for Set 3

For points $G(0,5)$ and $H(2,0)$:
$m_{GH}=\frac{0 - 5}{2-0}=\frac{-5}{2}$
For points $H(2,0)$ and $I(4,-5)$:
$m_{HI}=\frac{-5 - 0}{4 - 2}=\frac{-5}{2}$
Since $m_{GH}=m_{HI}$, points $G$, $H$, and $I$ are collinear.

Answer:

Set 1: $A(0,-3), B(2,-6), C(4,-9)$ and Set 3: $G(0,5), H(2,0), I(4,-5)$ are collinear.