The point halfway between the endpoints of a line segment is called the midpoint. Its y value is halfway between the two y values. Find the exact middle point in a line segment or a coordinate plane using the below given midpoint formula. 12 units along, and 5 units up. Mary Jane Sterling is the author of Algebra I For Dummies and many other For Dummies titles. When the endpoints of a line segment are known, we can find the point midway between them. , If we have coordinates (x₁,y₁) and (x₂,y₂), then the midpoint of these coordinates is determined by (x₁ + x₂)/2, (y₁ + y₂)/2. If you want to know the midpoint of the segment with endpoints (–4,–1) and (2,5), then plug the numbers into the midpoint formula, and you get a midpoint of (–1,2): See how this segment looks in graph form in the following figure. Step 2: Use the slope formula to show that the coordinate of the midpoint is located on the line segment. To use the midpoint formula, add the x-coordinates of the endpoints and divide the result by 2. The following video gives a proof of the midpoint formula using the Pythagorean Theorem. Home Algebra Linear Equations. Midpoint formula. Figure 1 Finding the coordinates of the midpoint of a line segment. To calculate it: Add both "x" coordinates, divide by 2. Mid Point Formula where (x 1, y 1, z 1) (x 2, y 2, z 2) be the end points of a line segment. P1 is a point on a line segment and P2 is a different point on the same line segment. The midpoint of this line is exactly halfway between these endpoints and its location can be found using the Midpoint Theorem, which states: The x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints. The The midpoint through M parallel to the y-axis bisects the segment A 1A2 at point M. M 1 is halfway form A 1 to A 2, the x-coordinate of M 1 is: x 1 + 1/2 ( x 2 - x 1) = x 1 + 1/2 x 2 - 1/2 x 1. yA+yB Find the coordinates of the midpoint of the line … Add both "y" coordinates, divide by 2. The midpoint is one that divides the segment into two equal segments. ). In Coordinate Geometry, midpoint theorem refers to the midpoint of the line segment. To find the midpoint of a line segment, you just calculate the averages of the coordinates — easy as pie. 2 ), M = ( So the answer is P = (1, –2). The midpoint is halfway between the two end points: Its x value is halfway between the two x values. The point M M is the midpoint of the line segment ¯¯¯¯¯ ¯AB A B ¯ if it is an element of the segment and divides it into two congruent segments, ¯¯¯¯¯¯ ¯AM ≅¯¯¯¯¯¯¯M B A M ¯ ≅ M B ¯. This forms a new coordinate you can call (x₃,y₃). In order to find the midpoint of a line segment, you first have to understand that it’s the point located on the exact midpoint of the 2 endpoints, so it’s the average of the endpoints. If you're seeing this message, it means we're having trouble loading external resources on our website. Again we want to find the x,y coordinate, that is directly in the middle of this line segment. To find the midpoint of a line segment, you calculate the two x coordinates' average to get the x-midpoint coordinate and the two y coordinates' average to get the y-midpoint coordinate. Midpoint Formula is used to find the point that is exactly halfway between two given points in a line segment. If the segment is horizontal or vertical, you can find the midpoint by dividing the length of the segment by 2 and counting that value from either of the endpoints. Just average the given x-coordinate values (x1, x2) and the y-coordinate values (y1, y2) to find the mid point of the line segment. Here the point (12,5) is Learn how to use the midpoint formula to find the midpoint of a line segment on the coordinate plane, or find the endpoint of a line segment given one point and the midpoint. Here Coordinates of A are (7,3) and B (-5,5) so, now substitute the right values into the midpoint formula. The midpoint calculator will solve this instantaneously if you input the coordinates. Example 2: If the midpoint of AB is (−3, 8) and A is (12, −1), find the coordinates of B. Let (x 1, y 1) and (x 2, y 2) represent the endpoints of a line segment. It defines the coordinate points of the midpoint of the line segment can be found by taking the average of the coordinates of the given endpoints.