Find The Midpoint Given Two Points Worksheet

6 problems

To find the midpoint between two points, identify the coordinates `(x_1, y_1)` and `(x_2, y_2)`, take the average of the `x`-coordinates and the average of the `y`-coordinates. The midpoint is the point with the calculated `x`-coordinate `(x_1 + x_2)/2` and `y`-coordinate `(y_1 + y_2)/2`.

Midpoint `= ((x_1 + x_2)/2, (y_1 + y_2)/2)`

This concept is widely used in various fields, including geometry, physics, and computer graphics.

Algebra 1
Coordinate Plane

How Will This Worksheet Titled "Find the Midpoint Given Two Points" Benefit Your Student's Learning?

  • Develops a clear understanding of what a midpoint is and how it is calculated.
  • Provides practice in using the midpoint formula to find the coordinates of the midpoint.
  • It helps students to find missing endpoints, determine fractional distances, or so...
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Solved Example

Q. K(2,9)K(2,9) and L(2,3)L(2,3) are the endpoints of a line segment. What is the midpoint MM of that line segment?
Solution:
  1. Midpoint Formula: Identify the midpoint formula for a line segment.\newlineThe midpoint is the average of the coordinates of the endpoints.\newlineMidpoint formula: \newlineM=(x1+x22,y1+y22)M = \left(\frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2}\right)
  2. Identify Endpoints: Endpoints: K(2,9)K(2, 9) and L(2,3)L(2, 3)\newline
  3. Substitute Coordinates:Substitute (2,9)(2, 9) for (x1,y1)(x_1, y_1) and (2,3)(2, 3) for (x2,y2)(x_2, y_2) into the midpoint formula.\newlineM=(2+22,9+32)M = \left(\frac{2 + 2}{2} , \frac{9 + 3}{2}\right)
  4. Calculate the Mid-point: Calculate the coordinates of MM.\newlineM=(2+22,9+32)M = \left(\frac{2 + 2}{2} , \frac{9 + 3}{2}\right)\newlineM=(42,122)M = \left(\frac{4}{2}, \frac{12}{2}\right)\newlineM=(2,6)M = (2, 6)

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