Calculate Horizontal and Vertical Distance
Calculating horizontal and vertical distance on a coordinate plane in Grade 6 uses the coordinates of two points: if the points are on opposite sides of an axis, add their absolute values; if on the same side, subtract. From enVision Mathematics, the distance between (-3, 2) and (5, 2) is |-3| + |5| = 3 + 5 = 8 because the points are on opposite sides of the y-axis. This absolute value approach avoids confusion with negative coordinates and builds the conceptual foundation for the distance formula in later geometry courses.
Key Concepts
The distance $d$ between two points on a horizontal or vertical line is found using their differing coordinates, $a$ and $b$: If the points are on opposite sides of an axis, add their absolute values: $d = |a| + |b|$. If the points are on the same side of an axis, subtract the smaller absolute value from the larger: $d = |\text{larger absolute value}| |\text{smaller absolute value}|$.
Common Questions
How do you find the horizontal distance between two points on a coordinate plane?
If the x-coordinates are on opposite sides of the y-axis, add their absolute values. If on the same side, subtract the smaller from the larger.
How do you find the vertical distance between two points?
If the y-coordinates are on opposite sides of the x-axis, add their absolute values. If on the same side, subtract the smaller from the larger.
Can you show an example with points on opposite sides?
Distance between (-3, 2) and (5, 2): the x-coordinates -3 and 5 are on opposite sides, so d = |-3| + |5| = 3 + 5 = 8.
Can you show an example with points on the same side?
Distance between (2, 1) and (7, 1): same side (both positive x), so d = 7 - 2 = 5.
Where is calculating horizontal and vertical distance covered in enVision Mathematics?
This skill is introduced in enVision Mathematics, Grade 6, as part of coordinate geometry and the number system content.
How does absolute value help with coordinate distance?
Absolute value ensures the distance is always positive, regardless of whether the coordinates are positive or negative. It measures the magnitude of the position without sign.
How does this connect to the distance formula in later math?
This horizontal/vertical distance skill is a special case of the full distance formula: d = √((x₂-x₁)² + (y₂-y₁)²), which is introduced in high school geometry.