# Coordinate Geometry: Straight Lines and Circles

### What's the Question?

What’s the Question? is an activity that can be used to act as stimuli for work on the geometry of straight lines and circles.

The activity consists of two mathematical diagrams. Students are asked to generate questions that could be asked related to each diagram.

The teacher notes give examples of the kinds of questions expected, provide teaching tips and suggest how the activity could be adapted.

### Connecting Perpendicular Lines A10

In this resource students identify perpendicular gradients and lines that are perpendicular, learn to relate their learning about perpendicular lines to their previous learning about straight lines and explain the reasons why lines are parallel and perpendicular. Students should have some knowledge of equations of straight lines, be able to identify parallel lines and use gradient triangles.

### Geometry

This resource covers aspects of geometry and are suitable for students studying mathematics at A Level. The topics covered include the **geometry of a circle**, polar coordinates, **the gradient and intercept of straight lines **and **properties of straight line segments**.

Comprehensive notes, with clear descriptions, for each resource are provided, together with relevant diagrams and examples. Students wishing to review, and consolidate, their knowledge and understanding of geometry will find them useful, as each topic includes a selection of questions to be completed, for which answers are provided.

### Coordinate Geometry

Three RISP activities covering a range of topics, each one having some activity which explores coordinate geometry.

**Circle Property**: Students generate two coordinates. The coordinates form the end points of the diameter of a circle. Students have to find the equation of the circle formed, compare their results with colleagues and explain their findings.

**Circles or Not?: **Students use a graph plotter to alter the coefficients of the equation of a circle and explore which values produce a circle and why.

**Tangents:** Explores the equation of a tangent to a quadratic. Students are asked to use a graph plotter to draw a quadratic graph of the form y=x2 + a2, then draw a line y=kx altering the value of k until the line is a tangent to the curve. Students then form a relationship between k and a

### Circle Geometry

Three advanced level lesson ideas from Susan Wall designed to explore the properties of circles and their equations. Each activity is accompanied by teacher notes suggesting how the activity could be delivered and possible extension ideas.

The first activity requires students to match the equations of circles to statements cards. There is not a unique solution to this problem thus requiring students to explain the mathematics used to justify their solution.

The second activity asks students to determine whether each of a number of statements is true or false. Once again students are required to justify their answer showing the mathematics they have used. In this exercise students are required to complete the square to rearrange the equation of the circle into a form that can be used to determine whether the statement is true or false.

The third activity contains a miscellany of probing questions which can be used in a variety of ways in the classroom in order to assess student understanding.