Achievement objective M71
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
M74, graphs
M72, solving equations
M77, and simultaneous equations
M78.
 See
key mathematical ideas on NZmaths.
Progression
M71 links from
GM67 and to
M81.
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 xaxis.
 Find the values of x that make lines joining (x,0), (2,1), and (6,4) as vertices of a rightangled triangle.
 Given the centre of a circle (2, 3) and the radius is 4, find the equation of the circle.

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+(y3)2 = 4
So, (x +2)2+(y3)2 = 42
(x +2)2+(y3)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.

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, 2 and 3 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.
The following achievement standard(s) could assess learning outcomes from this AO:
Last updated September 17, 2018
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