The distance between two points in the coordinate plane is the number of units between them. Let's explore two methods for calculating the horizontal distance between two points with the points and
Method 1
The distance between two points is the length of the line segment that connects them.
First, we plot the given points in the coordinate plane.
From the diagram, we see that the length of the segment is units, so the distance equals
Method 2
We can find the distance between the two points by finding the distance of each point from the -axis and then subtracting.
The point is at a distance of from the -axis, and the point is at a distance of from the -axis. Therefore, the distance between the two points is
What is the distance between the points and
Method 1
The distance between two points is the length of the line segment that connects them.
From the diagram, we see that the length of the segment is units, so the distance equals
Method 2
We can find the distance between the two points by finding the distance of each point from the -axis and then subtracting.
The point is at a distance of from the -axis, and the point is at a distance of from the -axis. Therefore, the distance between the two points is
What is the distance between the points $(-2,3)$ and $(-6,3)?$
|
a
|
$3$ |
|
b
|
$5$ |
|
c
|
$6$ |
|
d
|
$4$ |
|
e
|
$2$ |
What is the distance between the points $(1,3)$ and $(5,3)?$
|
a
|
$5$ |
|
b
|
$6$ |
|
c
|
$3$ |
|
d
|
$4$ |
|
e
|
$1$ |
What is the distance between the points and
Method 1
We plot the given points in the coordinate plane.
The distance between two points is the length of the line segment that connects them.
From the diagram, we see that the length of the segment is units, so the distance equals
Method 2
We can find the distance between the two points by finding the distance of each point from the -axis and then subtracting.
The point is at a distance of from the -axis, and the point is at a distance of from the -axis. Therefore, the distance between the two points is
What is the distance between the points $(6,-2)$ and $(6,-5)?$
|
a
|
$3$ |
|
b
|
$5$ |
|
c
|
$6$ |
|
d
|
$4$ |
|
e
|
$2$ |
What is the distance between the points $(4,2)$ and $(4,8)?$
|
a
|
$4$ |
|
b
|
$8$ |
|
c
|
$6$ |
|
d
|
$2$ |
|
e
|
$5$ |
When we want to find the distance between two points in different quadrants, method 1 works exactly the same, but method 2 is slightly different.
We can find the distance between the two points by finding the distance of each point from the -axis for a horizontal distance, or -axis for a vertical distance, and then adding.
So, what's the distance between and
Method 1
We plot the given points in the coordinate plane.
The distance between two points is the length of the line segment that connects them.
From the diagram, we see that the length of the segment is units, so the distance equals
Method 2
We can find the distance between the two points by finding the distance of each point from the -axis and then adding.
The point is at a distance of from the -axis, and the point is at a distance of from the -axis. Therefore, the distance between the two points is
What is the distance between the points and
Method 1
We plot the given points in the coordinate plane.
The distance between two points is the length of the line segment that connects them.
From the diagram, we see that the length of the segment is units, so the distance equals
Method 2
We can find the distance between the two points by finding the distance of each point from the -axis and then adding.
The point is at a distance of from the -axis, and the point is at a distance of from the -axis. Therefore, the distance between the two points is
What is the distance between the points $(3,2)$ and $(3,-4)?$
|
a
|
$2$ |
|
b
|
$6$ |
|
c
|
$7$ |
|
d
|
$3$ |
|
e
|
$4$ |
What is the distance between the points $(-3,-5)$ and $(1,-5)?$
|
a
|
$4$ |
|
b
|
$3$ |
|
c
|
$5$ |
|
d
|
$6$ |
|
e
|
$1$ |
