Solve the problem.
-Find the area of the triangle determined by the points P(1, 1, 1), Q( , -2, -8), and R(-8, 7, -3).
A) $\sqrt { 13774 }$
B) $\frac { \sqrt { 13774 } } { 2 }$
C) $\frac { \sqrt { 8590 } } { 2 }$
D) $\sqrt { 8590 }$

Question

Solve the problem.
-Find the area of the triangle determined by the points P(1, 1, 1), Q( , -2, -8), and R(-8, 7, -3). 
A) $\sqrt { 13774 }$
B) $\frac { \sqrt { 13774 } } { 2 }$
C) $\frac { \sqrt { 8590 } } { 2 }$
D) $\sqrt { 8590 }$

Quizplus · Accepted Answer

We can find the missing coordinate of point Q by noticing that the x-coordinate of Q is the same as the x-coordinate of R, which is -8. Therefore, the coordinates of Q are (-8, -2, -8). To find the area of the triangle, we can use the formula: area = 1/2 * |(P-Q) cross product (P-R)| where cross product is the vector cross product. Using the given coordinates, we can find the vectors: P-Q = <-7, 3, 7> and P-R = <-9, 6, -4> Taking the cross product, we get: (P-Q) cross product (P-R) = <-45, 35, 51> The magnitude of this vector is: |(P-Q) cross product (P-R)| = sqrt(45^2 + 35^2 + 51^2) = sqrt(13774) Multiplying by 1/2, we get the final answer: area = 1/2 * sqrt(13774) = sqrt(3443.5) = (B) sqrt(13774)/2

Solve the Problem 13774\sqrt { 13774 }13774​ B) 137742\frac { \sqrt { 13774 } } { 2 }213774​​

Solve the Problem $\sqrt { 13774 }$ B) $\frac { \sqrt { 13774 } } { 2 }$