Finding the Distance between Two Points (3.2.1)

Question 1

• The distance formula is an application of the Pythagorean Theorem, which states that the hypotenuse of a right triangle
equals the square root of the sum of the other sides squared.

Answer 1

• The distance formula is an application of the Pythagorean Theorem, which states that the hypotenuse of a right triangle
equals the square root of the sum of the other sides squared.

Question 2

• The midpoint formula determines the point in the middle of the line segment formed by 2 points.

Answer 2

• The midpoint formula determines the point in the middle of the line segment formed by 2 points.

Question 3

Draw your given line segment first.
Then draw a vertical line from one end and a horizontal line
from the other end. This creates a right triangle.
The length of the triangle’s horizontal side can be found by
taking the difference of the two x-values because they measure
horizontal movement.
The length of the vertical side can be found by taking the
difference of the two y-values because they measure vertical
movement.
Now, using the Pythagorean Theorem,
(first side)2
+ (second side)2
= (hypotenuse)2
.
. So,
Now that you know the formula, just substitute in the values
from each point and solve for your length.
It doesn’t matter which point is identified as (x1
, y1
) and (x2
,
y2
).
In this case (6, 4) is (x2
, y2
).
Finding the midpoint of a line segment means finding the
average between the two endpoints:
Add the x-values and divide by 2.
Add the y-values and divide by 2.
These answers are the ordered pair of your midpoint.

Answer 3

Draw your given line segment first.
Then draw a vertical line from one end and a horizontal line
from the other end. This creates a right triangle.
The length of the triangle’s horizontal side can be found by
taking the difference of the two x-values because they measure
horizontal movement.
The length of the vertical side can be found by taking the
difference of the two y-values because they measure vertical
movement.
Now, using the Pythagorean Theorem,
(first side)2
+ (second side)2
= (hypotenuse)2
.
. So,
Now that you know the formula, just substitute in the values
from each point and solve for your length.
It doesn’t matter which point is identified as (x1
, y1
) and (x2
,
y2
).
In this case (6, 4) is (x2
, y2
).
Finding the midpoint of a line segment means finding the
average between the two endpoints:
Add the x-values and divide by 2.
Add the y-values and divide by 2.
These answers are the ordered pair of your midpoint.