Question

Find the fourth vertex of the parallelogram whose consecutive vertices are (2, 4, -1), (3, 6, -1) and (4, 5, 1).

Answer 1

Step-by-step explanation:

Given Find the fourth vertex of the parallelogram whose consecutive vertices are (2, 4, -1), (3, 6, -1) and (4, 5, 1).

• Now a parallelogram ABCD is drawn .
• So the vertices are A(2,4,-1), B(3,6,-1) and C(4,5,1) and let D(x,y,z)
• In a parallelogram, the diagonals intersect each other.Let the point of intersection be p. AC and BD are the diagonals.
• So midpoint of AC = midpoint of BD
• So we have the midpoint formula for (x,y,z)
•             = (x1 + x2 / 2, y1 + y2 / 2, z1 + z2 / 2)
•             (2 + 4 / 2, 4 + 5 / 2, -1 + 1 / 2) = (3 + x / 2, 6 + y / 2, z + (- 1) / 2 )
• Now equating x,y and z terms we have,
•             2 + 4 / 2 = 3 + x / 2
•                 3 + x = 6
•                  x = 6 – 3
•                   x = 3
•            4 + 5 / 2 = 6 + y / 2
•                  6 + y = 9
•                      y = 9 – 6
•                     y = 3
•           -1 + 1 / 2 = z – 1 / 2
•                z – 1 = 0
•                 z = 0 + 1
•                 z = 1
• Therefore D(x,y,z) = D(3,3,1)

Reference link will be

https://brainly.in/question/7675695

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