Question

question 10 of 10
determine which set(s) of coordinates below are colinear.
set 1: a(0,6), b(2,3) and c(4,0)
set 2: d(0,3), e(2,0) and f(4, - 3)
set 3: g(0,3), h(4,0) and i(8, - 3)

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 slopes for Set 1

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

Step3: Calculate slopes for Set 2

For points $D(0,3)$ and $E(2,0)$, $m_{DE}=\frac{0 - 3}{2 - 0}=-\frac{3}{2}$.
For points $E(2,0)$ and $F(4,-3)$, $m_{EF}=\frac{-3 - 0}{4 - 2}=-\frac{3}{2}$.
Since $m_{DE}=m_{EF}$, points $D$, $E$, and $F$ are collinear.

Step4: Calculate slopes for Set 3

For points $G(0,3)$ and $H(4,0)$, $m_{GH}=\frac{0 - 3}{4 - 0}=-\frac{3}{4}$.
For points $H(4,0)$ and $I(8,-3)$, $m_{HI}=\frac{-3 - 0}{8 - 4}=-\frac{3}{4}$.
Since $m_{GH}=m_{HI}$, points $G$, $H$, and $I$ are collinear.

Answer:

Set 1: A(0,6), B(2,3) and C(4,0) are collinear; Set 2: D(0,3), E(2,0) and F(4,-3) are collinear; Set 3: G(0,3), H(4,0) and I(8,-3) are collinear.