Midpoint and Gradient of a Line Segment Interval on the Cartesian Plane (9)

Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software (ACMMG294)

LO: To find the mipoint and gradient of a line segment.
Know:

  • What an integer is
  • How to use co-ordinates to plot points.
  • What a midpoint of a line segment is
  • What the gradient of a line segment is.

Understand:

  • That the midpoint and gradient of a line segment can be found using formulas.

Do:

  • I can add integers.
  • I can find the gradient of a line segment.

Plotting Points for Line Segment

When we plot 2 points on a Cartesian Plane and then draw a straight line, we can easily find the distance between the two points.

To find the midpoint, it means to find the exact middle point of that line.

The formula for finding the midpoint in a line segment is:

Midpoint Worked Example

Calculating the Gradient of a Line Segment

A gradient of a line is also called a slope of a line. It basically means how steep is the line.

It can be found using the formula: rise divided by run.

In the case below, it rose 2 while only going across 1, which means this line has a slope (gradient) of 2.

Sometimes the slope (gradient) can go downwards towards the right, which makes the gradient (slope) negative.

Sometimes the slope (gradient) can be very steep (2), and sometimes it can be small (1/2). The higher the number for the slope the steeper the line is.

A horizontal line has a gradient (slope) of 0 because the rise is always 0. Zero divided by any number is always 0, which makes the gradient of a horizontal line always 0.


Midpoint Formula Videos

Gradient Videos

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