Achievement objective M7-1
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
- apply coordinate geometry techniques to points and lines.
Indicators
- Uses algebra and geometry to link points and lines on the Cartesian plane.
- Uses geometric features such as parallel lines, perpendicular lines, collinear points, centre, radius and diameter of circles, and types of triangles to prove conjectures.
- Makes links with trigonometry
M7-4, graphs
M7-2, solving equations
M7-7, and simultaneous equations
M7-8.
Progression
M7-1 links from GM6-7 and to M8-1.
What is new/changed?
- This was previously located in the geometry strand.
Possible context elaborations
- Prove a triangle is isosceles.
- Find the equation of a line parallel to or perpendicular to a given line.
- Find equations and points of intersections of lines such as medians and altitudes of a triangle.
- Prove given points are collinear.
- Find the centre of a circle, given 3 points on its circumference.
- Find the angle between lines by working with angles between line and x-axis.
- Find the values of x that make lines joining (x,0), (2,1), and (6,4) as vertices of a right-angled triangle.
- Given the centre of a circle (-2, 3) and the radius is 4, find the equation of the circle.
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Using the locus definition of a circle, the circle is the set of all points that are a distance 4 from (-2, 3). So the equation of the circle is all the points (x, y) such that:
√(x +2)2+(y-3)2 = 4
So, (x +2)2+(y-3)2 = 42
(x +2)2+(y-3)2 = 16 is the equation of the circle.
- Given that (-4, -1) and (6, 3) are the endpoints of a diameter of a circle, find the equation of the circle.
- Given that (2, -5) is a point on a circle with centre (3, 2), find the equation of the circle.
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Coordinate geometry: A couple of activities.
- Two towns: Find the distance between two points on a map. Find the place closest to the midpoint between the two towns.
Assessment for qualifications
NCEA achievement standards at level 1 and 2 have been aligned to the New Zealand Curriculum. Please ensure that you are using the correct version of the standards by going to the
NZQA website.
Aligned level 3 achievement standards will be registered by NZQA for use in 2013.
Full information on the level 3 draft standards and the alignment process can be found on
NCEA on TKI.
The following achievement standard(s) could assess learning outcomes from this AO.
- AS91256 Mathematics and statistics 2.1 Apply co-ordinate geometry methods in solving problems
Refer to the draft standards matrix.
Last updated September 26, 2012
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