Plot Points and Find Distances

In this lesson:

• Plot signed coordinates on a four-quadrant city map
• Recognize when two points share a coordinate
• Use absolute value to find segment length

What You Will Be Able to Do

By the end, you will:

1. Plot signed ordered pairs in all four quadrants
2. Recognize same-x and same-y point pairs
3. Compute for vertical segments
4. Compute for horizontal segments
5. Explain why absolute value is required

A Map of the Neighborhood

Your school sits at . East is positive , north is positive .

Each block is one unit. A signed pair tells you how far east or west, then how far north or south.

A city map is just a coordinate plane in disguise.

Four Locations on the Grid

Library , Park , Museum , Ice-cream .

Which Quadrant Is Each Location In?

Words to Coordinates

• Furthest east = largest
• Most southern = smallest (most negative)

You Try: Read the Locations

From the four points: Library , Ice-cream , Park , Museum .

1. Which is furthest east?
2. Which is most southern?
3. Which two share an east-west position?

From Plotting to Measuring

We can plot any pair. Now: how far apart are two plotted points?

We start with the easiest case — when the two points share one coordinate.

If two points share an or share a , the segment between them is straight along the grid.

Same x: A Vertical Segment

Plot and . Both sit on the line .

Count the Units

Start at , count up to .

That is 7 unit jumps. The segment has length .

The Same Count, Written with Absolute Value

Both subtraction orders give the same length. Absolute value picks the size, not the sign.

Why Absolute Value Is Required

Distance is a length. Lengths are never negative.

If your work gives , you skipped the . Add it back.

The minus sign is information about direction, not about size.

Same y: A Horizontal Segment

Plot and . Both sit on the line .

The Distance Rule

If two points share : distance (vertical).

If two points share : distance (horizontal).

Subtract the other coordinate — the one that differs.

A Common Slip: Negative Distance

Asked the distance from to , a student writes .

That is not the distance. is.

A negative answer is the alarm bell that was dropped.

Worked: Same x, and

Step 1. Same coordinate? Yes — both have .

Step 2. Subtract the other: .

Step 3. Absolute value: .

Distance = 7 units.

Worked: Same y, and

Step 1. Same coordinate? Yes — both have .

Step 2. Subtract the other: .

Step 3. Absolute value: .

Distance = 7 units.

Edge Case: A Coordinate Is Zero

Plot and . Both have — both sit on the -axis.

Sharing zero is sharing a coordinate.

You Try: to

Apply the three-step habit:

1. Same coordinate?
2. Subtract the other.
3. Take absolute value.

Check the Answer

Step 1. Same .

Step 2. .

Step 3. .

Distance = 5 units.

What We Built

• Same or same → segment runs along the grid
• Distance = differing coordinate's difference
• Absolute value = lengths are nonnegative

Up next: real city maps, navigation, and polygons whose sides are all axis-aligned.