Calculator UseThe midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint. Show Use this calculator to calculate the midpoint, the distance between 2 points, or find an endpoint given the midpoint and the other endpoint. Midpoint and Endpoint Calculator SolutionsInput two points using numbers, fractions, mixed numbers or decimals. The midpoint calculator shows the work to find:
The calculator also provides a link to the Slope Calculator that will solve and show the work to find the slope, line equations and the x and y intercepts for your given two points. How to Calculate the MidpointYou can find the midpoint of a line segment given 2 endpoints, (x1, y1) and (x2, y2). Add each x-coordinate and divide by 2 to find x of the midpoint. Add each y-coordinate and divide by 2 to find y of the midpoint. Calculate the midpoint, (xM, yM) using the midpoint formula: \( (x_{M}, y_{M}) = \left(\dfrac {x_{1} + x_{2}} {2} , \dfrac {y_{1} + y_{2}} {2}\right) \) It's important to note that a midpoint is the middle point on a line segment. A true line in geometry is infinitely long in both directions. But a line segment has 2 endpoints so it is possible to calculate the midpoint. A ray has one endpoint and is infinitely long in the other direction. Example: Find the MidpointSay you know two points on a line segment and their coordinates are (6, 3) and (12, 7). Find the midpoint using the midpoint formula. \( (x_{M}, y_{M}) = \left(\dfrac {x_{1} + x_{2}} {2} , \dfrac {y_{1} + y_{2}} {2}\right) \)
\( x_{M} = \dfrac {x_{1} + x_{2}} {2} \) \( x_{M} = \dfrac {6 + 12} {2} \) \( x_{M} = \dfrac {18} {2} \) \( x_{M} = {9} \) \( y_{M} = \dfrac {y_{1} + y_{2}} {2} \) \( y_{M} = \dfrac {3 + 7} {2} \) \( y_{M} = \dfrac {10} {2} \) \( y_{M} = {5} \) How to Calculate Distance Between 2 PointsIf you know the endpoints of a line segment you can use them to calculate the distance between the 2 points. Here you're actually finding the length of the line segment. Use the formula for distance between 2 points: \( d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2} \) The formula for distance between points is derived from the Pythagorean theorem, solving for the length of the hypotenuse. See our Pythagorean Theorem Calculator for a closer look. Example: Find the Distance Between 2 PointsYou know 2 points on a line segment and their coordinates are (13, 2) and (7, 10). Find the distance between the 2 points using the distance formula \( d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2} \)
\( d = \sqrt {(7 - 13)^2 + (10 - 2)^2} \) \( d = \sqrt {(-6)^2 + (8)^2} \) \( d = \sqrt {36 + 64} \) \( d = \sqrt {100} \) \( d = 10 \) Similar to this midpoint calculator is our Two Dimensional Distance Calculator. For distance between 2 points in 3 dimensions with (x, y, z) coordinates please see our 3 Dimension Distance Calculator. How to Calculate EndpointIf you know an endpoint and a midpoint on a line segment you can calculate the missing endpoint. Start with the midpoint formula from above and work out the coordinates of the unknown endpoint.
\( (x_{M}, y_{M}) = \left(\dfrac {x_{1} + x_{2}} {2} , \dfrac {y_{1} + y_{2}} {2}\right) \) \( x_{M} = \dfrac {x_{1} + x_{2}} {2} \) \( y_{M} = \dfrac {y_{1} + y_{2}} {2} \) Example: Find the EndpointUsing the steps above, let's find the endpoint of a line segment where we know one endpoint is (6, -4) and the midpoint is (1, 7). The endpoint is the (x1, y1) coordinate. The midpoint is the (xM, yM) coordinate.
\( (x_{M}, y_{M}) = \left(\dfrac {x_{1} + x_{2}} {2} , \dfrac {y_{1} + y_{2}} {2}\right) \) \( x_{2} = 2x_{M} - x_{1} \) \( y_{2} = 2y_{M} - y_{1} \) \( x_{2} = 2(1) - x_{1} \) \( y_{2} = 2(7) - y_{1} \) \( x_{2} = 2(1) - 6 \) \( y_{2} = 2(7) - (-4) \) \( x_{2} = 2 - 6 \) \( x_{2} = -4 \) \( y_{2} = 14 + 4 \) \( y_{2} = 18 \) What is the formula to find endpoint?The endpoint formula can be found by using algebraic methods to solve the midpoint formula for one endpoint. After working through the algebra, the formula for the Endpoint A A of line AB A B is (xa,ya)=((2xm−xb),(2ym−yb)) ( x a , y a ) = ( ( 2 x m − x b ) , ( 2 y m − y b ) ) .
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