MPM 2D GRADE 10 ACADEMIC
ANALYTIC GEOMETRY TEST 5
COM LEVEL
𝟏𝟎𝟎
K/U
𝟏𝟐
APP
𝟐𝟎
THI
𝟕
Day 1
Knowledge and Understanding [12 marks]
Show your full marks
1. AB is a line segment with the endpoints A (−𝟔. 𝟓, 𝟒) and B (𝟖. 𝟓, −𝟒).
Line AB represents Autumn Hill Blvd on the map. Each unit on the map
is equal to 1 km. Plot the line on the map.
Determine the midpoint of AB, plot the midpoint on the grid and label it
C. This point is a fire hydrant on a town map. [4 marks]
2. Determine the length of Autumn Hill Blvd. Round your answer to the
nearest km and record the length on the map. [4 marks]
3. Draw a circle around Autumn Hill Blvd so that each end point of
Autumn Hill Blvd lies inside the circle. Label your circle and determine
its equation. [4 marks]
Application [6 marks]
4. A school has been built at a point D(𝟐, −𝟔). Plot the school and
name it SLSS (STEPHEN LEWIS SECONDARY SCHOOL). Draw the median DC from
the school to Autumn Hill Blvd and label the line with the name Pleasant
Ridge. Determine the equation of DC [6 marks]
5. A Pizza-Pizza has been built close enough to school so that the
students, who have a car, can quickly go by lunch. This Pizza-Pizza has
been placed at (−𝟐, −𝟒). Plot the Pizza Pizza on the map.
A shortest road needs to be made from Pizza-Pizza to Pleasant Ridge.
Draw the new road on the map. Label the point where the new road and
Pizza Pizza meet as F. Determine the shortest distance between Pizza
Pizza and Pleasant Ridge, rounded to one decimal place. [10 marks]
6. Your family has decided to move near SLSS. You new house is at
(𝟐, −𝟒). Plot it on the map and label it “house”. Determine whether or
not your new house lies on Pleasant Ridge. [4 marks]
Thinking
7. Three traffic lights are to be put on Autumn Hill Blvd at equal
distances from the end points but not including the end points. What are
the coordinates of the three traffic lights? Show all your work and
explain your thinking for full marks. [7 marks]
Day 2
COM LEVEL:
K/U:
𝟗
APP:
Thinking Level:
𝟏𝟓
1. Consider triangle ABC with vertices 𝐴(−1, 0), 𝐵(0, −3) and 𝐶 (5, 2).
a) Classify the triangle. Ensure to show all your work and conclude your
findings. [K/U – 7 marks]
b) Verify that the length of the median from A is equal to half the length
of side BC. [APP – 5 marks]
2. Given the vertices 𝐴(−3, 2), 𝐵(−1, 0), 𝐶 (−3, −2) and 𝐷 (−5, 0).
a) Describe a plan to verify at least 3 different geometric properties
using at least 3 of the given vertices. [Thinking Level]
b) Verify one of your listed geometric properties above [APP – 5
marks]
3. Consider the circle with equation 𝑥 2 + 𝑦 2 = 25.
a) State the radius and the coordinates of the center of the circle [K/U –
2 marks]
b) If the center of the initial circle shifted to be (−2, 3), determine six
points on the circle and clearly explain your thinking / reasoning.
[Thinking Level]
c) Choose two of the six points found in part b) to form a chord. Verify
that the right bisector of the chord passes through the center of the circle.
[APP – 5 marks]