A focused Grade 6 learning session for Distance on the Coordinate Plane using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving distance on the coordinate plane.
Distance on the Coordinate Plane means choosing a model, naming what each number means, and explaining the strategy.
Question: What is the distance between \((1,2)\) and \((5,2)\)?
Why it works: The points share the same \(y\)-coordinate \((2)\), so the distance is the difference of the \(x\)-coordinates: \(|5-1|=4\) units.
Answer: \(4\) units
Question: Find the distance between \((3,0)\) and \((3,5)\).
Answer: \(5\) units
Question: What is the distance from \((0,2)\) to \((5,2)\)?
Answer: \(5\) units
Question: On a grid, a store is at \((2,4)\) and a home is at \((10,4)\). The scale is \(1\) unit \(= 50\) meters. What is the actual distance?
Why it works: Distance on grid: \(|10-2|=8\) units. Actual distance: \(8 \times 50 = 400\) meters.
Answer: \(400\) m
Distance on the Coordinate Plane becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Understand the model before choosing the operation.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
What is the distance between the points \((2,3)\) and \((2,-5)\) on the coordinate plane?
Answer D: \(8\) units
The points share the \(x\)-coordinate, so the distance is the difference of the \(y\)-coordinates: \(|3-(-5)|=|3+5|=8\) units.
What is the distance between \((1,2)\) and \((5,2)\)?
Answer D: \(4\) units
The points share the same \(y\)-coordinate \((2)\), so the distance is the difference of the \(x\)-coordinates: \(|5-1|=4\) units.
What is the distance between the points \((-3,4)\) and \((-3,-2)\) on the coordinate plane?
Answer C: \(6\) units
The \(x\)-coordinates are the same, so subtract the \(y\)-coordinates: \(|4-(-2)|=|4+2|=6\) units.
Points \(P(0,-2)\) and \(Q(6,-2)\) are plotted on a coordinate plane. What is the distance from \(P\) to \(Q\)?
Answer C: \(6\) units
Same \(y\)-coordinate \((-2)\): \(|6-0|=6\) units.
What is the horizontal distance between \((1,3)\) and \((5,3)\)?
Answer B: \(4\) units
Same \(y\)-coordinate: \(|5-1|=4\) units.
The distance between points \((4,5)\) and \((4,y)\) is \(7\) units. The points have the same \(x\)-coordinate. What could \(y\) be?
Answer B: \(y=-2\) or \(y=12\)
Since \(|5-y|=7\), then \(y=5-7=-2\) or \(y=5+7=12\).
Find the distance between \((3,0)\) and \((3,5)\).
Answer C: \(5\) units
Same \(x\)-coordinate \((3)\): \(|5-0|=5\) units.
Points \(A(-2,1)\) and \(B(4,1)\) lie on a coordinate plane. What is the distance between them?
Answer C: \(6\) units
Same \(y\)-coordinate \((1)\): \(|4-(-2)|=|4+2|=6\) units.
What is the distance from \((0,2)\) to \((5,2)\)?
Answer C: \(5\) units
Same \(y\)-coordinate \((2)\): \(|5-0|=5\) units.
A rectangle has vertices at \((1,1)\), \((5,1)\), \((5,4)\), and \((1,4)\). What is the perimeter of this rectangle?
Answer A: \(14\) units
Length is \(|5-1|=4\) units and width is \(|4-1|=3\) units. The perimeter is \(2(4+3)=14\) units.
A rectangle has vertices at \((1,1)\), \((5,1)\), \((5,4)\), and \((1,4)\). What is the perimeter?
Answer D: \(14\) units
Length: \(|5-1|=4\) units. Width: \(|4-1|=3\) units. Perimeter: \(2(4+3)=14\) units.
