Finding Lengths on the Coordinate Plane
Horizontal & Vertical Lines on a
Coordinate Plane
Finding Lengths of Horizontal Lines on
a Coordinate Plane
• Horizontal Lines have the same y-coordinate
– Example: (2, 1) and (5, 1)
• If points are on the opposite sides of the y-axis,
then they have different signs.
– Example: (2, 1) and (-3, 1)
Horizontal - Points on the Same Side
• Points on the same side of the y-axis
• Same side = same sign!
– To find the length
• Count the distance between the x-coordinates (or
subtract them)
– Example: (2, 1) and (5, 1)
• The distance from 2 to 5 = 3, so the distance is 3 units.
• 5–2=3
Horizontal - Points on the Opposite Side
• Points on the opposite side of the y-axis
• Opposite side = Opposite signs
– To find the length
• Find the Absolute Value of each of the x-coordinates
• Add the two absolute values
– Example: (2, 1) and (-3, 1)
• 2 and -3 are on opposite sides. Absolute values are 2 & 3
•
, so the distance between the points is 5 units.
Finding Lengths of Vertical Lines on a
Coordinate Plane
• Vertical Lines have the same x-coordinate
– Example: (2, 4) and (2, 9)
• If points are on the opposite sides of the x-axis,
then they have different signs.
– Example: (-5, 4) and (-5, -2)
Vertical - Points on the Same Side
• Points on the same side of the x-axis
• Same side = same sign!
– To find the length
• Count the distance between the y-coordinates (or
subtract them)
– Example: (-1, 6) and (-1, 4)
• The distance from 4 to 6 = 2, so the distance is 2 units.
• 6–4=2
Vertical - Points on the Opposite Side
• Points on the opposite side of the x-axis
• Opposite side = Opposite signs
– To find the length
• Find the Absolute Value of each of the y-coordinates
• Add the two absolute values
– Example: (5, 4) and (5, 2)
• Since 4 is a positive and 2 is a negative, the points are on
opposite sides of the axis.
is 4 + 2
• 4 + 2 = 6, so the distance between the two points is 6 units
Lines and No lines
 Neither Horizontal or Vertical
• Points with different x-coordinates and different y-coordinates
do not form a horizontal or vertical line.
– Example: (-3, 2) and (5, 6)
 Lie on the X-axis
• Points that lie on the x-axis and have a y-coordinate of 0.
– Example: (8, 0) and (7, 0)
 Lie on the Y-axis
• Points that lie on the y-axis and have an x-coordinate of 0.
– Example: (0, 4) and (0, 10)