SOLUTION: Determine weather triangle QRS is a right triangle for the given vertices. Explain Q(18,13) R(17,-3) S(-18,12) select one: a. a. no; QR = sqrt(257), QS = sqrt(1297), RS = sqrt(

Algebra ->  Triangles -> SOLUTION: Determine weather triangle QRS is a right triangle for the given vertices. Explain Q(18,13) R(17,-3) S(-18,12) select one: a. a. no; QR = sqrt(257), QS = sqrt(1297), RS = sqrt(      Log On


   

Question 1088408: Determine weather triangle QRS is a right triangle for the given vertices. Explain Q(18,13) R(17,-3) S(-18,12)
select one:
a. a. no; QR = sqrt(257), QS = sqrt(1297), RS = sqrt(558) QR2+QS2≠ RS2
b. yes; QR = sqrt(257), QS = sqrt(1297), RS = sqrt(558) RS2+QS2= RQ2
c. yes; QR = sqrt(257), QS = sqrt(1297), RS = sqrt(558) QR2+QS2≠ RS2
d. no; QR = sqrt(257), QS = sqrt(1297), RS = sqrt(558) RS2+QS2≠ RQ2
Found 2 solutions by MathLover1, Boreal:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Determine weather triangle QRS is a right triangle for the given vertices. Explain Q(18,13) R(17,-3) S(-18,12)
sketch triangle first:

RS is hypotenuse if triangle QRS is a right triangle
find the length: S(-18,12) to R(17,-3)
RS=sqrt%28%28-18-17%29%5E2%2B%2812-%28-3%29%29%5E2%29
RS=sqrt%28%28-35%29%5E2%2B15%5E2%29
RS=sqrt%281450%29
RS=sqrt%2825%2A58%29
RS=5sqrt%2858%29

legs should be: QR and QS
Q(18,13) to R(17,-3)
QR=sqrt%28%2818-17%29%5E2%2B%2813-%28-3%29%29%5E2%29
QR=sqrt%281%5E2%2B%2813%2B3%29%5E2%29
QR=sqrt%281%2B16%5E2%29
QR=sqrt%28257%29
Q(18,13) to S(-18,12)
QS=sqrt%28%2818-%28-18%29%29%5E2%2B%2813-12%29%5E2%29
QS=sqrt%28%2818%2B18%29%5E2%2B%281%29%5E2%29
QS=sqrt%2836%5E2%2B1%29
QS=sqrt%281296%2B1%29
QS=sqrt%281297%29
check if: %28SR%29%5E2=%28QR%29%5E2%2B%28QS%29%5E2
%285sqrt%2858%29%29%5E2=%28sqrt%28257%29%29%5E2%2B%28sqrt%281297%29%29%5E2
1450=257%2B1297
1450%3C%3E1554=> proves that triangle QRS is not a right triangle
because
a.
QR=sqrt%28257%29
QS=sqrt%281297%29
RS=5sqrt%2858%29
%28SR%29%5E2%3C%3E%28QR%29%5E2%2B%28QS%29%5E2




Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Using distance formula sqrt (difference in x^2+difference in y ^2)
QR is sqrt (257)
RS is sqrt (1225+225)=sqrt (1450)
QS is sqrt (1296+1)=sqrt (1297)
square QR (257) add to it QS squared (1297) and get squared RS (1450).
No.
But choices show RS as sqrt (558) it isn't given the difference in RS x which is -35 and -35^2=1225 and difference in RS y which is 15^2=225
slope of QS is (1/36)
slope of QR is 16
slope of RS is (-15/35) or -(3/7)
None of those 3 gives a negative reciprocal, so no perpendicular lines.