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Victoriag2626
13.03.2020 •
Mathematics
A triangle has vertices P(2,−1,0),Q(4,1,1),R(4,−5,4). Determine if the triangle is a right triangle (a) Using the Pythagorean theorem; (b) Using the properties of the dot product.
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Ответ:
see answers below
Step-by-step explanation:
a) using the Pythagorean theorem
PQ= (2,−1,0) - (4,1,1) = (-2,-2,-1)
QR= (4,1,1) - (4,−5,4) = (0,6,-3)
RP= (4,−5,4) - (2,−1,0) = (2,-4,4)
then
length 1 = |PQ| = √[(-2)²+(-2)²+(-1)²]= √9 = 3
length 2 = |QR| = √[(0)²+(6)²+(-3)²]= √45
length 3 = |RP| = √[(2)²+(-4)²+(-4)²]= √36 = 6
then if the triangle is a right triangle
length 2 = √[(length 1)²+ (length 3)²] = √(3²+6²) = √45
then our assumption is correct
b) using the properties of dot product
PQ * RP = (-2,-2,-1) * (2,-4,4) = 2*(-2) + (-2)*(-4) + (-1)*4 = -4 + 8 - 4 = 0
thus PQ is perpendicular to RP . Then the triangle PQR is a right one
Ответ:
Step-by-step explanation:
The answer is D. Easy way to tell, the less than or equal to sign indicates a solid line in the graph. Equal=solid line. Also when you solve for y, the slope of the line (-2/3)is negative, indicating a line sloping downward.