Coordinate Geometry
Plotting points, distance, midpoint, and slope on the coordinate plane — excludes graphing linear equations (see linear-graphing)
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Imagine a giant treasure map with a grid covering the whole thing. That's exactly what a coordinate plane is! 🗺️ When you play video games like Minecraft, your character moves around using coordinates to find rare diamonds or build awesome castles. In math, we call this Coordinate Geometry. It's really just a fancy way of saying "finding stuff on a grid."
The grid has two main roads. The x-axis goes left and right, like a flat street. The y-axis goes up and down, like a tall elevator. Every point on the map has a special address, written as (x, y). You always walk along the flat street (the x number) before you take the elevator up or down (the y number). A great trick to remember this is: you have to run before you can jump! 🏃♂️
On the SSAT, you'll get to play detective on this grid. You might need to figure out the shape of a fenced-in yard by plotting its corners. Or, you might need to find the exact middle of a pizza delivery route (we call that the midpoint). Sometimes, you'll calculate how far a superhero flew from point A to point B (the distance). It might look tricky at first glance, but once you know how to read the map, you'll be racking up points on the test like a pro gamer! 🎮 Grab your pencils, and let's explore the math map together!
Practice Questions
3 practice questions for SSAT Middle Level
(3, 1) (3, 7) (1, 3) Show Solution
- Moving to the right on a coordinate plane increases the x-coordinate, so add 5 to the starting x-coordinate: . Moving down decreases the y-coordinate, so subtract 3 from the starting y-coordinate: . The new coordinates of the game token are
(3, 1).
(4, 5) (5, 4) Show Solution
- A rectangle's sides are parallel to the x-axis and y-axis. The given x-coordinates are and . The given y-coordinates are and . The given points form the bottom-left , top-left , and bottom-right corners. The fourth vertex must be the top-right corner, which will share the x-coordinate of the bottom-right point () and the y-coordinate of the top-left point (). Therefore, the fourth vertex is located at
(4, 5).
(1, 3). From the library, she walks straight east to the park, located at (6, 3). If each unit on the grid represents 1 mile, what is the total distance Sarah walked?Show Solution
- First, calculate the distance Sarah walked from her house to the library. Since the x-coordinates are the same, subtract the y-coordinates to find the vertical distance: miles. Next, calculate the distance from the library to the park. Since the y-coordinates are the same, subtract the x-coordinates to find the horizontal distance: miles. Finally, add the two distances together to find the total distance walked: miles.
Tips & Strategies
- Always draw a quick sketch! ✏️ If the SSAT asks you about a shape or distance, draw a tiny grid and plot the points. Seeing it visually often makes the answer obvious.
- Remember 'Run before you jump!' Always read the x-coordinate (left/right) first, then the y-coordinate (up/down). Mixing these up is a trap the test makers love to set.
- Look out for the 3-4-5 right triangle! When finding the distance between two points, if the x-distance is 3 and the y-distance is 4 (or vice versa), the total distance is always 5.
Common Mistakes
- Watch out for mixing up your x and y coordinates! Plotting
(2, 5)instead of(5, 2)will land you in a completely different spot on the map. 🛑 - Don't forget that distance can never be negative! Even if you subtract backwards and get a negative number, the length of a line is always a positive number.
Frequently Asked Questions
Do I need to memorize the big, scary distance formula for the SSAT?
Not necessarily! For most SSAT distance problems, you can just draw a right triangle on a grid and use the Pythagorean theorem (). It's much easier to remember and does the exact same thing!
What if my midpoint isn't a whole number?
That is totally okay! Sometimes the middle of a pizza slice is a fraction. 🍕 If your average gives you a decimal like or a fraction like , just leave it! The answer choices on the test will match your math.
Are coordinate geometry questions on all levels of the SSAT?
Yes! Lower level tests focus mostly on plotting points and identifying shapes like squares and rectangles. Upper level tests will ask you to calculate distance, midpoint, and slope.