Distance, Midpoint, & Gradient - Exercises | IB Math AISL | Perplex

Distance, Midpoint, & Gradient

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Distance between two points, midpoint of two points, and finding gradient using two points

Want a deeper conceptual understanding? Try our interactive lesson!

Cartesian Plane

2. Prior learning

The Cartesian Plane is 2 dimensional surface, where positions represent coordinates of the form (x,y). The cartesian plane has

an x-axis: a horizontal line where y=0
a y-axis: a vertical line where x=0.
the origin: where the two axes meet. Both x and y are zero here, so its coordinates are (0,0)

The coordinates (x,y) of a point tell you how far along the x-axis the point is, and how far along the y-axis the point is. By convention, positive x coordinates are to the right of the origin, and positive y-coordinates above the origin. Similarly, negative x and y coordinates are to the left of and below the origin, respectively.

Cartesian quadrants

2. Prior learning

The x and y axes divide the coordinate plane into 4 regions called quadrants. They are often labeled with roman numerals I,II,III and IV.

Quadrant	x	y
I	positive	positive
II	negative	positive
III	negative	negative
IV	positive	negative

Distance between 2 points

2. Prior learning

The distance between two points (x1,y1) and (x2,y2) is given by

d=√(x1−x2)2+(y1−y2)2📖

Midpoint of 2 points

2. Prior learning

The coordinates of the midpoint of two points is

(2x1+x2,2y1+y2)📖

Slope as rise over run

SL Core 2.1

The gradient of the line is a measure of its steepness. It is calculated by measuring the rise (change in y) in the line over a certain run (change in x).

The gradient of the line passing through the points (x1,y1) and (x2,y2) is

m=x2−x1y2−y1📖

Nice work completing Distance, Midpoint, & Gradient, here's a quick recap of what we covered:

Skills covered

Mixed Practice

Exercises checked off

I'm Plex, here to help you understand this concept!

Equations of a Line

Cartesian plane & lines

Distance, Midpoint, & Gradient

0 of 0 exercises completed

Distance between two points, midpoint of two points, and finding gradient using two points

Want a deeper conceptual understanding? Try our interactive lesson!

Cartesian Plane

2. Prior learning

The Cartesian Plane is 2 dimensional surface, where positions represent coordinates of the form (x,y). The cartesian plane has

an x-axis: a horizontal line where y=0
a y-axis: a vertical line where x=0.
the origin: where the two axes meet. Both x and y are zero here, so its coordinates are (0,0)

Cartesian quadrants

2. Prior learning

The x and y axes divide the coordinate plane into 4 regions called quadrants. They are often labeled with roman numerals I,II,III and IV.

Quadrant	x	y
I	positive	positive
II	negative	positive
III	negative	negative
IV	positive	negative

Distance between 2 points

2. Prior learning

The distance between two points (x1,y1) and (x2,y2) is given by

d=√(x1−x2)2+(y1−y2)2📖

Midpoint of 2 points

2. Prior learning

The coordinates of the midpoint of two points is

(2x1+x2,2y1+y2)📖

Slope as rise over run

SL Core 2.1

The gradient of the line is a measure of its steepness. It is calculated by measuring the rise (change in y) in the line over a certain run (change in x).

The gradient of the line passing through the points (x1,y1) and (x2,y2) is

m=x2−x1y2−y1📖

Nice work completing Distance, Midpoint, & Gradient, here's a quick recap of what we covered:

Skills covered

Mixed Practice

Exercises checked off

I'm Plex, here to help you understand this concept!