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: \(y=mx+b\)

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Level 1: Slope

Problem 1

Find the slope between \((2,3)\) and \((6,11)\).

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Use the slope formula.

\[ m=\frac{y_2-y_1}{x_2-x_1} \] \[ m=\frac{11-3}{6-2} \] \[ m=\frac{8}{4}=2 \]

The slope is \(2\).

Problem 2

Find the slope between \((-1,4)\) and \((3,-2)\).

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\[ m=\frac{-2-4}{3-(-1)} \] \[ m=\frac{-6}{4} \] \[ m=-\frac{3}{2} \]

The slope is \(-\frac{3}{2}\).

Problem 3

Find the slope between \((5,2)\) and \((5,9)\).

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\[ m=\frac{9-2}{5-5} \] \[ m=\frac{7}{0} \]

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 \((5,5)\).

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Use the distance formula.

\[ d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \] \[ d=\sqrt{(5-1)^2+(5-2)^2} \] \[ d=\sqrt{4^2+3^2} \] \[ d=\sqrt{16+9}=5 \]

The distance is \(5\).

Problem 5

Find the distance between \((-2,1)\) and \((4,9)\).

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\[ d=\sqrt{(4-(-2))^2+(9-1)^2} \] \[ d=\sqrt{6^2+8^2} \] \[ d=\sqrt{36+64} \] \[ d=10 \]

The distance is \(10\).

Problem 6

Find the distance between \((0,0)\) and \((3,-4)\).

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\[ d=\sqrt{(3-0)^2+(-4-0)^2} \] \[ d=\sqrt{3^2+(-4)^2} \] \[ d=\sqrt{9+16}=5 \]

The distance is \(5\).

Level 3: Midpoint Formula

Problem 7

Find the midpoint between \((2,4)\) and \((8,10)\).

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Use the midpoint formula.

\[ \left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right) \] \[ \left(\frac{2+8}{2},\frac{4+10}{2}\right) \] \[ (5,7) \]

The midpoint is \((5,7)\).

Problem 8

Find the midpoint between \((-3,6)\) and \((7,-2)\).

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\[ \left(\frac{-3+7}{2},\frac{6+(-2)}{2}\right) \] \[ \left(\frac{4}{2},\frac{4}{2}\right) \] \[ (2,2) \]

The midpoint is \((2,2)\).

Level 4: Equations of Lines

Problem 9

Write the equation of a line with slope \(3\) and \(y\)-intercept \(-2\).

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Use slope-intercept form.

\[ y=mx+b \] \[ y=3x-2 \]

Problem 10

Write the equation of a line with slope \(-\frac{1}{2}\) passing through \((4,1)\).

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Start with \(y=mx+b\).

\[ y=-\frac{1}{2}x+b \]

Substitute \((4,1)\).

\[ 1=-\frac{1}{2}(4)+b \] \[ 1=-2+b \] \[ b=3 \] \[ y=-\frac{1}{2}x+3 \]

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.

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