Chapter 13
Coordinate Geometry
If two parks are marked on a map, how can you decide exactly how far apart they are without measuring the picture? A drawing helps you see a shape, but its appearance alone cannot settle every question. Coordinate geometry asks what the positions of points can tell us about the figures they form. How much can a few numbers reveal that a sketch only suggests?
What You'll Explore
6 lessons.
Progress can't be saved in this browser, so lesson statuses can't be set here.
-
Two points on a grid may look close together, but how can you know their exact separation or locate the point halfway between them? Revisit these familiar questions and investigate the geometric reasons behind the coordinate methods you already know.
-
Suppose a meeting place must lie along a straight path, closer to one end than the other. How can coordinates describe its location when the two parts must have a particular ratio, and why does the order of the endpoints matter?
-
Lines drawn on a grid may appear parallel or seem to meet at a right angle, but a picture can mislead. What coordinate evidence settles these relationships, and what geometric reasoning stands behind familiar slope rules?
-
Could coordinates help prove a statement about a whole family of quadrilaterals? Explore what makes a coordinate argument convincing, along with the questions that arise when a polygon's perimeter and area need to be measured.
-
A circle equation may look familiar, but what can it tell you about a line that seems to just touch the circle? Investigate how an algebraic description can support a geometric claim that a drawing alone cannot prove.
-
Where might a curve come from if we begin with a question about distances instead of an equation? Return to the familiar parabola and investigate what a fixed point and a fixed straight line have to do with its shape.