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Build the Distance Formula from the Picture

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Orienting Yourself: The Use of Coordinates · Distance and reflection · 4:04

You'll learn: Generalise coordinate differences and derive the square-root distance expression.

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Build the Distance Formula from the Picture

4:04

Playing

Build the Distance Formula from the Picture

You'll learn: Generalise coordinate differences and derive the square-root distance expression.

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Same topic

Distance and reflection

5

Find Distances Along Horizontal and Vertical Lines
3:54
Find Distances Along Horizontal and Vertical Lines
You'll learn: Recognise equal x- or y-coordinates and use the absolute difference of the other coordinates.
Find a Slanting Distance by Building a Right Triangle
3:45
Find a Slanting Distance by Building a Right Triangle
You'll learn: Turn horizontal and vertical shifts into perpendicular legs and find direct distance.
Use the Distance Formula to Measure a Triangle
3:50
Use the Distance Formula to Measure a Triangle
You'll learn: Apply the formula to all three sides and interpret exact square-root lengths.
Why the Distance Formula Works with Negative Coordinates
4:02
Why the Distance Formula Works with Negative Coordinates
You'll learn: Subtract negative coordinates and explain why reversing endpoint order preserves distance.
Reflect a Triangle: What Changes and What Stays the Same?
3:50
Reflect a Triangle: What Changes and What Stays the Same?
You'll learn: Track coordinate changes under reflection in either axis and compare side lengths.

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Applications

5

Predict a Shape Before Plotting Its Points
3:41
Predict a Shape Before Plotting Its Points
You'll learn: Predict axis-parallel sides, perpendicular sides and mirror points before checking the graph.
Build a Right Triangle Around a Given Point
3:50
Build a Right Triangle Around a Given Point
You'll learn: Construct a valid right triangle using a given vertex and calculate its three sides.
Can a Street Address Identify More Than One Crossing?
4:14
Can a Street Address Identify More Than One Crossing?
You'll learn: Test whether a street-index convention identifies a unique crossing and why direction information matters.
Do Two Circular Icons Fit and Overlap on a Screen?
4:40
Do Two Circular Icons Fit and Overlap on a Screen?
You'll learn: Check circle extents against screen boundaries and compare centre distance with the radii.
Is This Tilted Quadrilateral Really a Square?
4:12
Is This Tilted Quadrilateral Really a Square?
You'll learn: Use distances to justify the shape and determine its area.

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Challenge explorations

5

Are Three Points on One Straight Line?
4:20
Are Three Points on One Straight Line?
You'll learn: Use distance addition to test collinearity, then plot both sets to verify.
Build Isosceles Triangles Using Coordinates
4:06
Build Isosceles Triangles Using Coordinates
You'll learn: Construct the two requested triangle types and verify their properties.
What Makes a Point the Midpoint?
4:28
What Makes a Point the Midpoint?
You'll learn: Check that a midpoint lies on the segment and divides it equally. Discover coordinate averages.
Find a Missing Endpoint from the Midpoint
4:12
Find a Missing Endpoint from the Midpoint
You'll learn: Reverse the coordinate-average relationship to find an unknown endpoint.
Divide a Segment into Three Equal Parts
4:00
Divide a Segment into Three Equal Parts
You'll learn: Extend equal division from halves to thirds and find both internal division points.