Solve problems about shapes whose corners are given as coordinates: lengths by Pythagoras, midpoints and centres, missing corners, areas by the box method, and naming a quadrilateral from its vertices.
What you will learn
- Find the length of a line segment from its end points with Pythagoras
- Use midpoints for the centre of a circle and the crossing point of diagonals
- Find the fourth corner of a parallelogram
- Find the area of a shape with corners on grid points
- Name a quadrilateral from gradients and squared lengths
- Find a missing coordinate from a length
A length is the long side of a right-angled triangle
Between two points, go across and then up.
Those two steps are the short sides of a right-angled triangle, and the line segment is its longest side. So square the two steps, add, and take the square root. Subtract the coordinates to get the steps; a negative step is fine, because squaring makes it positive.
- A(−2, 1) and B(4, 9)
- across: 4 − (−2) = 6, up: 9 − 1 = 8
- AB² = 6² + 8² = 36 + 64 = 100
- AB = √100 = 10
The slip to avoid: adding the steps (6 + 8 = 14). That is the walk along the grid lines, which is always longer than the straight line.
The rest of this lesson and its 10 practice questions are locked.
In this lesson
- A length is the long side of a right-angled triangle
- Midpoints, centres and missing corners
- Areas: draw the box, take away the corners
- Naming a shape from its coordinates
- Working backwards from a length
- Try it: First question
10 practice questions, marked as you go; about 30 minutes in all.
Key terms
Across, Gradients, Squared lengths
In this unit: Graphs and coordinates: shapes on axes, regions, areas and tangents
More graphs and coordinate geometry: shapes on coordinate axes, gradients and perpendicular lines in shapes, regions with strict and inclusive boundaries, the area under a curve from trapezia, and the gradient at a point from a tangent.
- Shapes on coordinate axes
- Gradients and lines in shapes
- Regions in depth
- Area under a curve
- Gradient at a point, and the kinematics formulae
All of Graphs and coordinates: shapes on axes, regions, areas and tangents