# Midpoint

The midpoint is the point that is **halfway** between 2 given points.

**Midpoint = ** | **(x**_{1} + x_{2}) | ** , ** | **(y**_{1} + y_{2}) |

**2** | **2** |

## Example One - Midpoint

What is the midpoint between the points (2,1) and (4,5)?

**Answer:**

(x_{1}, y_{1}) = (2,1)

(x_{2}, y_{2}) = (4,5)

Midpoint = | (x_{1} + x_{2}) | , | (y_{1} + y_{2}) |

2 | 2 |

Midpoint = | (2 + 4) | , | (1 + 5) |

2 | 2 |

Midpoint = (3,3)

## Questions - Find the Midpoint

**Q1.** (2,5) and (6, 10)

**Q2.** (–3, –5) and (–7, 9)

**Answers**

**A1.** (4 , 7.5)

**A2.** (–5, 2)

## X-Intercept

The x-intercept is the point at which a graph crosses the x-axis.

The **y-coordinate at the x-intercept is 0**.

## Example Two - X-Intercept

Find the x-intercept of the graph of y = x + 3.

**Answer:**

y = x – 3

0 = x – 3

x = 3

The coordinates of the x-intercept are (3,0)

## Y-Intercept

The y-intercept is the point at which a graph crosses the y-axis.

The **x-coordinate at the y-intercept is 0**.

## Example Three - Y-Intercept

Find the y-intercept of the graph of y = x + 3.

**Answer:**

y = x – 3

y = 0 – 3

y = –3

The coordinates of the x-intercept are (0,–3)

## Questions - Intercepts

**Q1.** Find the x-intercept of y = 5x + 3.

**Q2.** Find the y-intercept of y = 4x – 8.

**Answers**

**A1.** 3

**A2.** 2