Coordinate Geometry Practice Worksheet
Practice slope, distance formula, midpoint formula, and equations of lines with step-by-step solutions.
Try each problem on your own first. Then click Show solution to check the formula, substitution, and final answer.
Coordinate Geometry Formulas
- Slope: \(m=\frac{y_2-y_1}{x_2-x_1}\)
- Distance: \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
- Midpoint: \(\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\)
- Slope-intercept form: \(y=mx+b\)
Level 1: Slope
Problem 1
Find the slope between \((2,3)\) and \((6,11)\).
Show solution
Use the slope formula.
The slope is \(2\).
Problem 2
Find the slope between \((-1,4)\) and \((3,-2)\).
Show solution
The slope is \(-\frac{3}{2}\).
Problem 3
Find the slope between \((5,2)\) and \((5,9)\).
Show solution
Since division by zero is undefined, the slope is undefined. This is a vertical line.
Level 2: Distance Formula
Problem 4
Find the distance between \((1,2)\) and \((5,5)\).
Show solution
Use the distance formula.
The distance is \(5\).
Problem 5
Find the distance between \((-2,1)\) and \((4,9)\).
Show solution
The distance is \(10\).
Problem 6
Find the distance between \((0,0)\) and \((3,-4)\).
Show solution
The distance is \(5\).
Level 3: Midpoint Formula
Problem 7
Find the midpoint between \((2,4)\) and \((8,10)\).
Show solution
Use the midpoint formula.
The midpoint is \((5,7)\).
Problem 8
Find the midpoint between \((-3,6)\) and \((7,-2)\).
Show solution
The midpoint is \((2,2)\).
Level 4: Equations of Lines
Problem 9
Write the equation of a line with slope \(3\) and \(y\)-intercept \(-2\).
Show solution
Use slope-intercept form.
Problem 10
Write the equation of a line with slope \(-\frac{1}{2}\) passing through \((4,1)\).
Show solution
Start with \(y=mx+b\).
Substitute \((4,1)\).
Need more help with coordinate geometry?
Coordinate geometry becomes easier when students can carefully organize ordered pairs and choose the correct formula. For a full explanation, visit my Coordinate Geometry guide.