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Coordinate Geometry (Easy)

AMC 10 Q1–8 depth — contest entry, not school drills.

EasyMediumHardAIME / USAJMO / AMO

Coordinate Geometry: core idea

Distance/slope.

Example problem: hint and answer

Find the slope of the line through (1,2)(1,2) and (5,10)(5,10).

Hint: Use slope, midpoint, or distance formulas directly. Answer: 2.

Practice (9 problems — type your answers)

  • 1. Find the distance between (0,0)(0,0) and (3,4)(3,4).

  • 2. Find the midpoint of (2,3)(2,3) and (8,7)(8,7) as an ordered pair.

  • 3. What is the yy-intercept of y=3x−7y=3x-7?

  • 4. Find the equation's slope: 4x−2y=84x-2y=8.

  • 5. A point (x,5)(x,5) lies on y=2x+1y=2x+1. Find xx.

  • 6. Find the area of the rectangle with opposite vertices (1,2)(1,2) and (6,6)(6,6).

  • 7. Reflect (3,−4)(3,-4) across the xx-axis. Give the new yy-coordinate.

  • 8. Find the xx-intercept of y=−2x+8y=-2x+8.

  • 9. What is the slope of a line perpendicular to y=13x+2y=\frac13x+2?

Coordinate Geometry Practice Problems — Easy