This answer key shows the full solution for each test question and explains how the 20 points are awarded. Partial credit is given when a student sets up the distance or reflection correctly but makes one sign error.
Question 1: Name the quadrant (2 points)
a) Negative \(x\) and positive \(y\): Quadrant II.
b) Positive \(x\) and negative \(y\): Quadrant IV.
Scoring: 1 point for each correct quadrant.
Question 2: Plot points (2 points)
A: move 3 right and 4 down. B: move 5 left and 2 down. Both points are in Quadrant IV and Quadrant III, respectively.
Scoring: 1 point for each point plotted in the correct place and labeled.
Question 3: Read ordered pairs (3 points)
Read left or right first, then up or down.
a) \((-4, 3)\) b) \((2, 5)\) c) \((-1, -3)\)
Scoring: 1 point for each correct ordered pair. Reversed coordinates earn no point.
Question 4: Reflect a point (2 points)
a) The x-axis changes the sign of \(y\): \((-3, -7)\).
b) The y-axis changes the sign of \(x\): \((3, 7)\).
Scoring: 1 point for each correct reflection.
Question 5: Distance between points (2 points)
a) Same x-coordinate, so use y. \(-2\) and \(6\) are on opposite sides of 0: \(|-2| + |6| = 8\). 8 units.
b) Same y-coordinate, so use x. \(9\) and \(-3\) are on opposite sides of 0: \(|9| + |-3| = 12\). 12 units.
Scoring: 1 point for each correct distance.
Question 6: Rectangle on the plane (3 points)
a) \(D\) has the same x-coordinate as \(A\) and the same y-coordinate as \(C\): \(D(-4, 2)\).
b) \(AB = |-4| + |3| = 7\) and \(BC = |-3| + |2| = 5\). 7 units and 5 units.
c) \(2(7 + 5) = \)24 units.
Scoring: 1 point for each part.
Question 7: Walking route (3 points)
a) Same x-coordinate: \(|-4| + |5| = 9\) blocks.
b) Same y-coordinate: \(|-6| + |3| = 9\) blocks.
c) \(9 + 9 = 18\) blocks.
a) 9 blocks b) 9 blocks c) 18 blocks
Scoring: 1 point for each part.
Question 8: Find the error (3 points)
The points have the same y-coordinate, so the distance comes from the x-coordinates. But \(-3\) and \(5\) are on opposite sides of 0, so Jamal should add the absolute values instead of subtracting the numbers. He treated \(-3\) as 3.
\(|-3| + |5| = 3 + 5 = 8\).
The correct distance is 8 units.
Scoring: 1 point for explaining that the points are on opposite sides of 0; 1 point for using absolute values correctly; 1 point for 8.
20 points
See every chapter on the Grade 6 math page.