a) 9,12,15
b) 10.4
c) -3/2
Step-by-step explanation:
Step 1 :
a)
If the square of the highest length of line equals the sum of square of the other 2 length, then the 3 length can form a right triangle
Using this ,
1) 9,12,15
[tex]15^{2} = 225\\\\9^{2} +12^{2} = 225[/tex]
Hence this forms a right triangle
2)3,5,7
[tex]7^{2} =49\\\\3^{2} + 5^{2} = 34\\[/tex]
Hence this cannot form a right triangle
3)5,7,8.9
[tex](8.9)^{2} = 79.21\\\\5^{2}+7^{2} = 74\\[/tex]
This cannot form a right triangle
4)2,9,11
[tex]11^{2} = 121\\\\9^{2} + 2^{2} = 84[/tex]
Hence this cannot form a right triangle
Step 2 :
Length of the given line segment can be found using [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} } \\[/tex]
So for the given points the length is
[tex]\ \sqrt{(3-(-7))^{2} + (4-1)^{2} }[/tex] = 10.4
Step 3 :
The slope of the given line is
m = (-7-(-4)/5-3 = -3/2
