Page 50 - Math 9-10 (2009)

PRINCIPLES OF MATHEMATICS, GRADE 10, ACADEMIC (MPM2D) 49
Analytic Geometry
Overall Expectations
By the end of this course, students will:
• model and solve problems involving the intersection of two straight lines;
• solve problems using analytic geometry involving properties of lines and line segments; • verifygeometricpropertiesoftrianglesandquadrilaterals,usinganalyticgeometry.
Specific Expectations
Using Linear Systems to Solve Problems
By the end of this course, students will:
– solve systems of two linear equations involving two variables, using the algebraic method of substitution or elimination
(Sample problem: Solve y = x – 5,
3x + 2y = –2 for x and y algebraically, and
verify algebraically and graphically);
– solve problems that arise from realistic sit- uations described in words or represented by linear systems of two equations involv- ing two variables, by choosing an appro- priate algebraic or graphical method (Sample problem: The Robotics Club raised $5000 to build a robot for a future competition. The club invested part of the money in an account that paid 4% annual interest, and the rest in a government bond that paid 3.5% simple interest per year. After one year, the club earned a total of $190 in interest. How much was invested at each rate?Verify your result.).
Solving Problems Involving
Properties of Line Segments
By the end of this course, students will:
– develop the formula for the midpoint of a line segment, and use this formula to solve problems (e.g., determine the coordinates of the midpoints of the sides of a triangle, given the coordinates of the vertices, and verify concretely or by using dynamic geometry software);
– develop the formula for the length of a line segment, and use this formula to solve problems (e.g., determine the lengths of the line segments joining the midpoints of the sides of a triangle, given the coordi- nates of the vertices of the triangle, and verify using dynamic geometry software);
– develop the equation for a circle with centre (0, 0) and radius r, by applying the formula for the length of a line segment;
– determine the radius of a circle with cen- tre (0, 0), given its equation; write the equation of a circle with centre (0, 0), given the radius; and sketch the circle, given the equation in the form x2+y2=r2;
– solve problems involving the slope, length, and midpoint of a line segment (e.g., determine the equation of the right bisec- tor of a line segment, given the coordinates of the endpoints; determine the distance from a given point to a line whose equa- tion is given, and verify using dynamic geometry software).
Using Analytic Geometry to
Verify Geometric Properties
By the end of this course, students will:
– determine, through investigation (e.g., using dynamic geometry software, by paper folding), some characteristics and properties of geometric figures (e.g., medians in a triangle, similar figures con- structed on the sides of a right triangle);
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