A parallelogram has vertices A(4,4,-1),B(5,6, | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given,$ABCD$ is a parallelogram with vertices $A(4,4,-1)$,$B(5,6,-1)$,$C(6,5,1)$ and $D(x, y, z)$.We know that the diagonals of a parallelogram $A

Vedclass · Accepted Answer

$(5,3,1)$

Vedclass · Answer

(C) Given,$ABCD$ is a parallelogram with vertices $A(4,4,-1)$,$B(5,6,-1)$,$C(6,5,1)$ and $D(x, y, z)$.We know that the diagonals of a parallelogram $ABCD$ bisect each other.Therefore,the mid-point of $AC$ = mid-point of $BD$.$\left(\frac{4+6}{2}, \frac{4+5}{2}, \frac{-1+1}{2}\right) = \left(\frac{x+5}{2}, \frac{y+6}{2}, \frac{z-1}{2}\right)$$\left(\frac{10}{2}, \frac{9}{2}, 0\right) = \left(\frac{x+5}{2}, \frac{y+6}{2}, \frac{z-1}{2}\right)$On comparing both sides,we get:$\frac{x+5}{2} = \frac{10}{2}$ $\Rightarrow x+5 = 10$ $\Rightarrow x = 5$$\frac{y+6}{2} = \frac{9}{2}$ $\Rightarrow y+6 = 9$ $\Rightarrow y = 3$$\frac{z-1}{2} = 0$ $\Rightarrow z-1 = 0$ $\Rightarrow z = 1$Thus,the vertex $D(x, y, z)$ is $(5, 3, 1)$.

$A$ parallelogram has vertices $A(4,4,-1)$,$B(5,6,-1)$,$C(6,5,1)$ and $D(x, y, z)$. Then the vertex $D$ is

Similar Questions

Which of the following statements are true?

$ABCD$ is a parallelogram,$P$ is the mid-point of $AB$. If $R$ is the point of intersection of $AC$ and $DP$,then $R$ divides $AC$ internally in the ratio

The points $(-2, 4, 7)$,$(3, -6, -8)$,and $(1, -2, -2)$ are:

If the mid-points of the sides $AB, BC, CA$ of a triangle are $(1, 5, -1), (0, 4, -2), (2, 3, 4)$ respectively,then the length of the median drawn from $C$ to $AB$ is

If $A(0,4,0)$,$B(0,0,3)$,and $C(0,4,3)$ are the vertices of $\Delta ABC$,then its incentre is

Vedclass Test Series

Exam Paper Generator

Online Exam Module