SOLUTION: The three vertices of a triangle are as follows: (-4,5),(-4,-3), and (2,-3). Give the length of the longest of the longest side. Give your answer as a simplified radical.

Algebra ->  Triangles -> SOLUTION: The three vertices of a triangle are as follows: (-4,5),(-4,-3), and (2,-3). Give the length of the longest of the longest side. Give your answer as a simplified radical.       Log On


   

Question 934596: The three vertices of a triangle are as follows:
(-4,5),(-4,-3), and (2,-3).
Give the length of the longest of the longest side.
Give your answer as a simplified radical.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
first find the distance between given points:
(-4,5) and (-4,-3)

Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (-4, 5), we can say (x1, y1) = (-4, 5)
So x%5B1%5D+=+-4, y%5B1%5D+=+5


Since the second point is (-4, -3), we can also say (x2, y2) = (-4, -3)
So x%5B2%5D+=+-4, y%5B2%5D+=+-3


Put this all together to get: x%5B1%5D+=+-4, y%5B1%5D+=+5, x%5B2%5D+=+-4, and y%5B2%5D+=+-3

--------------------------------------------------------------------------------------------


Now use the distance formula to find the distance between the two points (-4, 5) and (-4, -3)



d+=+sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2+%2B+%28y%5B1%5D+-+y%5B2%5D%29%5E2%29


d+=+sqrt%28%28-4+-+%28-4%29%29%5E2+%2B+%285+-+%28-3%29%29%5E2%29 Plug in x%5B1%5D+=+-4, y%5B1%5D+=+5, x%5B2%5D+=+-4, and y%5B2%5D+=+-3


d+=+sqrt%28%28-4+%2B+4%29%5E2+%2B+%285+%2B+3%29%5E2%29


d+=+sqrt%28%280%29%5E2+%2B+%288%29%5E2%29


d+=+sqrt%280+%2B+64%29


d+=+sqrt%2864%29


d+=+8

==========================================================

Answer:


The distance between the two points (-4, 5) and (-4, -3) is exactly 8 units





(-4,5) and (2,-3)

Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (-4, 5), we can say (x1, y1) = (-4, 5)
So x%5B1%5D+=+-4, y%5B1%5D+=+5


Since the second point is (2, -3), we can also say (x2, y2) = (2, -3)
So x%5B2%5D+=+2, y%5B2%5D+=+-3


Put this all together to get: x%5B1%5D+=+-4, y%5B1%5D+=+5, x%5B2%5D+=+2, and y%5B2%5D+=+-3

--------------------------------------------------------------------------------------------


Now use the distance formula to find the distance between the two points (-4, 5) and (2, -3)



d+=+sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2+%2B+%28y%5B1%5D+-+y%5B2%5D%29%5E2%29


d+=+sqrt%28%28-4+-+%282%29%29%5E2+%2B+%285+-+%28-3%29%29%5E2%29 Plug in x%5B1%5D+=+-4, y%5B1%5D+=+5, x%5B2%5D+=+2, and y%5B2%5D+=+-3


d+=+sqrt%28%28-4+-+2%29%5E2+%2B+%285+%2B+3%29%5E2%29


d+=+sqrt%28%28-6%29%5E2+%2B+%288%29%5E2%29


d+=+sqrt%2836+%2B+64%29


d+=+sqrt%28100%29


d+=+10

==========================================================

Answer:


The distance between the two points (-4, 5) and (2, -3) is exactly 10 units






(-4,-3)and (2,-3)

Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (-4, -3), we can say (x1, y1) = (-4, -3)
So x%5B1%5D+=+-4, y%5B1%5D+=+-3


Since the second point is (2, -3), we can also say (x2, y2) = (2, -3)
So x%5B2%5D+=+2, y%5B2%5D+=+-3


Put this all together to get: x%5B1%5D+=+-4, y%5B1%5D+=+-3, x%5B2%5D+=+2, and y%5B2%5D+=+-3

--------------------------------------------------------------------------------------------


Now use the distance formula to find the distance between the two points (-4, -3) and (2, -3)



d+=+sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2+%2B+%28y%5B1%5D+-+y%5B2%5D%29%5E2%29


d+=+sqrt%28%28-4+-+%282%29%29%5E2+%2B+%28-3+-+%28-3%29%29%5E2%29 Plug in x%5B1%5D+=+-4, y%5B1%5D+=+-3, x%5B2%5D+=+2, and y%5B2%5D+=+-3


d+=+sqrt%28%28-4+-+2%29%5E2+%2B+%28-3+%2B+3%29%5E2%29


d+=+sqrt%28%28-6%29%5E2+%2B+%280%29%5E2%29


d+=+sqrt%2836+%2B+0%29


d+=+sqrt%2836%29


d+=+6

==========================================================

Answer:


The distance between the two points (-4, -3) and (2, -3) is exactly 6 units





as you can see,
the distance between the two points (-4, 5) and (-4, -3) is exactly 8 units
the distance between the two points (-4, 5) and (2,+-3) is exactly 10 units
the distance between the two points (-4,+-3) and (2,+-3) is exactly 6 units

so, the length of the longest of the longest side is 10