How to Use Distance Formula to Find the Length of a Line
Set up the Distance Formula., Find the coordinates of the line segment’s endpoints., Plug the coordinates into the Distance Formula., Calculate the subtraction in parentheses., Square the value in parentheses., Add the numbers under the radical...
Step-by-Step Guide
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Step 1: Set up the Distance Formula.
The formula states that d=(x2−x1)2+(y2−y1)2{\displaystyle d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}}}, where d{\displaystyle d} equals the distance of the line, (x1,y1){\displaystyle (x_{1},y_{1})} equal the coordinates of the first endpoint of the line segment, and (x2,y2){\displaystyle (x_{2},y_{2})} equal the coordinates of the second endpoint of the line segment., These might already be given.
If not, count along the x-axis and y-axis to find the coordinates.
The x-axis is the horizontal axis; the y-axis is the vertical axis.
The coordinates of a point are written as (x,y){\displaystyle (x,y)}.
For example, a line segment might have an endpoint at (2,1){\displaystyle (2,1)} and another at (6,4){\displaystyle (6,4)}. , Be careful to substitute the values for the correct variables.
The two x{\displaystyle x} coordinates should be inside the first set of parentheses, and the two y{\displaystyle y} coordinates should be inside the second set of parentheses.
For example, for points (2,1){\displaystyle (2,1)} and (6,4){\displaystyle (6,4)}, your formula would look like this: d=(6−2)2+(4−1)2{\displaystyle d={\sqrt {(6-2)^{2}+(4-1)^{2}}}} , By using the order of operations, any calculations in parentheses must be completed first.
For example:d=(6−2)2+(4−1)2{\displaystyle d={\sqrt {(6-2)^{2}+(4-1)^{2}}}}d=(4)2+(3)2{\displaystyle d={\sqrt {(4)^{2}+(3)^{2}}}} , The order of operations states that exponents should be addressed next.
For example:d=(4)2+(3)2{\displaystyle d={\sqrt {(4)^{2}+(3)^{2}}}}d=16+9{\displaystyle d={\sqrt {16+9}}} , You do this calculation as if you were working with whole numbers.
For example:d=16+9{\displaystyle d={\sqrt {16+9}}}d=25{\displaystyle d={\sqrt {25}}} , To reach your final answer, find the square root of the sum under the radical sign.
Since you are finding a square root, you may have to round your answer.
Since you are working on a coordinate plane, your answer will be in generic “units,” not in centimeters, meters, or another metric unit.
For example:d=25{\displaystyle d={\sqrt {25}}}d=5{\displaystyle d=5} units -
Step 2: Find the coordinates of the line segment’s endpoints.
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Step 3: Plug the coordinates into the Distance Formula.
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Step 4: Calculate the subtraction in parentheses.
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Step 5: Square the value in parentheses.
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Step 6: Add the numbers under the radical sign.
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Step 7: Solve for d{\displaystyle d}.
Detailed Guide
The formula states that d=(x2−x1)2+(y2−y1)2{\displaystyle d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}}}, where d{\displaystyle d} equals the distance of the line, (x1,y1){\displaystyle (x_{1},y_{1})} equal the coordinates of the first endpoint of the line segment, and (x2,y2){\displaystyle (x_{2},y_{2})} equal the coordinates of the second endpoint of the line segment., These might already be given.
If not, count along the x-axis and y-axis to find the coordinates.
The x-axis is the horizontal axis; the y-axis is the vertical axis.
The coordinates of a point are written as (x,y){\displaystyle (x,y)}.
For example, a line segment might have an endpoint at (2,1){\displaystyle (2,1)} and another at (6,4){\displaystyle (6,4)}. , Be careful to substitute the values for the correct variables.
The two x{\displaystyle x} coordinates should be inside the first set of parentheses, and the two y{\displaystyle y} coordinates should be inside the second set of parentheses.
For example, for points (2,1){\displaystyle (2,1)} and (6,4){\displaystyle (6,4)}, your formula would look like this: d=(6−2)2+(4−1)2{\displaystyle d={\sqrt {(6-2)^{2}+(4-1)^{2}}}} , By using the order of operations, any calculations in parentheses must be completed first.
For example:d=(6−2)2+(4−1)2{\displaystyle d={\sqrt {(6-2)^{2}+(4-1)^{2}}}}d=(4)2+(3)2{\displaystyle d={\sqrt {(4)^{2}+(3)^{2}}}} , The order of operations states that exponents should be addressed next.
For example:d=(4)2+(3)2{\displaystyle d={\sqrt {(4)^{2}+(3)^{2}}}}d=16+9{\displaystyle d={\sqrt {16+9}}} , You do this calculation as if you were working with whole numbers.
For example:d=16+9{\displaystyle d={\sqrt {16+9}}}d=25{\displaystyle d={\sqrt {25}}} , To reach your final answer, find the square root of the sum under the radical sign.
Since you are finding a square root, you may have to round your answer.
Since you are working on a coordinate plane, your answer will be in generic “units,” not in centimeters, meters, or another metric unit.
For example:d=25{\displaystyle d={\sqrt {25}}}d=5{\displaystyle d=5} units
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Lauren Gonzales
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