Question

chu plotted 3 points on a grid. the 3 points were all on the same straight line. if she plots another point on the line, what could be its coordinates? a. (2,5) b. (4,4) c. (6,3) d. (7,3)

Explanation:

Step1: Find the slope between two - points

Let the points be \((1,6)\), \((3,5)\), \((5,4)\). Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), taking \((x_1,y_1)=(1,6)\) and \((x_2,y_2)=(3,5)\), we have \(m=\frac{5 - 6}{3 - 1}=\frac{-1}{2}=-\frac{1}{2}\).

Step2: Check each option

For option A \((2,5)\): Taking \((x_1,y_1)=(1,6)\) and \((x_2,y_2)=(2,5)\), \(m=\frac{5 - 6}{2 - 1}=- 1
eq-\frac{1}{2}\).
For option B \((4,4)\): Taking \((x_1,y_1)=(3,5)\) and \((x_2,y_2)=(4,4)\), \(m=\frac{4 - 5}{4 - 3}=-1
eq-\frac{1}{2}\).
For option C \((6,3)\): Taking \((x_1,y_1)=(5,4)\) and \((x_2,y_2)=(6,3)\), \(m=\frac{3 - 4}{6 - 5}=-1
eq-\frac{1}{2}\).
For option D \((7,3)\): Taking \((x_1,y_1)=(5,4)\) and \((x_2,y_2)=(7,3)\), \(m=\frac{3 - 4}{7 - 5}=-\frac{1}{2}\).

Answer:

D. \((7,3)\)