**High School Number Sense Lesson 48: Finding the Midpoint between 2 Points**

Imagine a line segment on a graph that joins two points. Today we will discover how to find the midpoint of that imaginary line segment, or the point exactly halfway between those two points. This concept appeared

**8 times**last year, with a median placement at

**question # 48**.

**Number Dojo Level: 246**

First, we need to understand that in geometry, the location of a point is represented as an

**ordered pair**, such as (x, y).

**x**is the x-coordinate (also known as the

**abscissa**), and

**y**is the y-coordinate (also known as the

**ordinate**).

- The
**abscissa**tells us how far the point is from the y-axis (left if negative, right if positive). - The
**ordinate**tells us how far the point is from the x-axis (below if negative, above if positive).

**3 units left**of the y-axis and

**2 units above**the x-axis. The

**origin**is the point at (0, 0)--where the x-axis and y-axis intersect.

**How to Solve:**

- To find the midpoint's
**abscissa**, take the average of the two endpoints' abscissas. - To find the midpoint's
**ordinate**, take the average of the two endpoints' ordinates.

**Example 1: The x-coordinate of the midpoint of the points (3, 7) and (1, 5) is ___**

- Take the average of the two x-coordinates: 3 and 1.
- The answer is
**2**.

**Example 2: The y-coordinate of the midpoint of the line segment between (4, 5) and (0, 8) is ___**

- Take the average of the two y-coordinates: 5 and 8.
- The answer is
**6.5**.

**Example 3: The abscissa of the midpoint of the line segment between (5, 3) and (-3, 6) is ___**

- Take the average of the two abscissas (x-coordinates): 5 and -3.
- The answer is
**1**.

**Example 4: The ordinate of the midpoint of the line segment between (-3, -8) and (1, -3) is ___**

- Take the average of the two ordinates (y-coordinates): -8 and -3.
- The answer is
**-5.5**.

**Example 5: The midpoint of the segment with endpoints (6, 2) and (-1, 5) is (x, y). Find x + y.**

- The average of the x-coordinates is (6 + -1)/2 =
**2.5**. - The average of the y-coordinates is (2 + 5)/2 =
**3.5**. - 2.5 + 3.5 =
**6**.

**Example 6: The midpoint of the segment with endpoints (x, y) and (3, 1) is (-2, 5). Find x + y.**

- This one is a little trickier. The average of x and 3 is -2, and those two coordinates are 5 apart. So x must be -2 - 5 =
**-7**. - The average of y and 1 is 5, and those two coordinates are 4 apart. So y must be 5 + 4 =
**9**. - x + y = -7 + 9 =
**2**.

**Here's a free worksheet to help you practice Midpoint2Pts:**

midpoint2pts.pdf |

**Up Next for High School: Inequality**