Question

which of the following points is collinear with (1, 1), and (2, 2)?
○ (3, 3)
○ (5, 6)
○ (3, 2)
○ (4, 1)

Explanation:

Step1: Find the slope between \((1,1)\) and \((2,2)\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For points \((x_1,y_1)=(1,1)\) and \((x_2,y_2)=(2,2)\), \(m=\frac{2 - 1}{2 - 1}=1\).

Step2: Check the slope for each option

• For \((3,3)\): Using the slope formula with \((1,1)\) and \((3,3)\), \(m=\frac{3 - 1}{3 - 1}=\frac{2}{2}=1\).
• For \((5,6)\): Using the slope formula with \((1,1)\) and \((5,6)\), \(m=\frac{6 - 1}{5 - 1}=\frac{5}{4}

eq1\).

• For \((3,2)\): Using the slope formula with \((1,1)\) and \((3,2)\), \(m=\frac{2 - 1}{3 - 1}=\frac{1}{2}

eq1\).

• For \((4,1)\): Using the slope formula with \((1,1)\) and \((4,1)\), \(m=\frac{1 - 1}{4 - 1}=0

eq1\).

Answer:

\((3,3)\)