Use the Distance Formula to calculate the lengths of the segments formed by the given points.
No, see solution.
Practice makes perfect
We will begin with calculating the lengths of the segments formed by the given points. Let's use the Distance Formula.
d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)
We can calculate the lengths of JK, KL, and JL by substituting the coordinates of the given points into this formula.
Points
Substitute
Simplify
Segment Length
J(- 7,- 1) and K(9,- 5)
JK=sqrt((9-(- 7))^2+(- 5-(- 1))^2)
JK=sqrt(256+16)
JK≈ 16.5
K(9,- 5) and L(21,- 8)
KL=sqrt((21-9)^2+(- 8-(- 5))^2)
KL=sqrt(144+9)
KL≈ 12.4
J(- 7,- 1) and L(21,- 8)
JL=sqrt((21-(- 7))^2+(- 8-(- 1))^2)
JL=sqrt(900+49)
JL≈ 30.8
Now, let's recall what the Triangle Inequality Theorem states.
The sum of the lengths of any two
sides of a triangle must be greater
than the length of the third side.
We can add each pair of two lengths of the sides and compare the sum with the length of the third side.
Chose Two Sides
Sum
Third Side
Comparison
JK and KL
16.5+12.4=28.9
JL=30.8
28.9 < 30.8
KL and JL
12.4+30.8=43.2
JK=16.5
43.2 > 16.5
JK and JL
16.5+30.8=47.3
KL=12.4
47.3 > 12.4
We can see that the theorem is not satisfied for the first pair of sides. Therefore, the given coordinates are not the vertices of a triangle.
