We will begin by finding the distances between each pair of points. Then, we can order the line segments from longest to shortest.
Finding the Distances
To determine the distance between two points, we can use the Distance Formula. First, let's calculate the distance between A(- 6,1) and B(- 1,6). To do it, we will substitute the coordinates of these points into the formula.
We found that the distance between the points A and B is 5sqrt(2). Let's calculate the distances between the other pairs of points in the same way.
Points (x_1,y_1), (x_2,y_2)
sqrt((x_2-x_1)^2+(y_2-y_1)^2)
Simplify
Distance
a. A( - 6, 1), B( - 1, 6)
sqrt(( - 1-( - 6)) ^2 +( 6- 1)^2)
sqrt(50)
AB=5sqrt(2)
b. C( - 5, 8), D( 5, 8)
sqrt(( 5-( - 5)) ^2 +( 8- 8)^2)
sqrt(100)
CD=10
c. E( 2, 7), F( 4, - 2)
sqrt(( 4- 2)^2+( - 2- 7) ^2)
sqrt(85)
EF=sqrt(85)
d. G( 7, 3), H( 7, - 1)
sqrt(( 7- 7)^2+( - 1- 3) ^2)
sqrt(16)
GH=4
e. J( - 4, - 2), K( 1, - 5)
sqrt(( 1-( - 4))^2+( - 5-( - 2)) ^2)
sqrt(34)
JK=sqrt(34)
f. L( 3, - 8), M( 7, - 5)
sqrt(( 7- 3)^2+( - 5-( - 8)) ^2)
sqrt(25)
LM=5
Ordering the Line Segments
Finally, we will order the line segments from longest to shortest. To compare their lengths we will focus only on the radical expressions in the third column of our table. Comparing them is equivalent to comparing the values under the radicals.
100>85>50>34>25>16
⇕
sqrt(100)>sqrt(85)>sqrt(50)>sqrt(34)>sqrt(25)>sqrt(16)
Knowing this, we can order the segments from longest to shortest.
