If the three vertices of a rectangle taken in | vedclass

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

Question

(C) Let the vertices of the rectangle be $A(2, -2)$,$B(8, 4)$,$C(5, 7)$,and $D(x, y)$.Since the diagonals of a rectangle bisect each other,the midpoin

Vedclass · Accepted Answer

$(-1, 1)$

Vedclass · Answer

(C) Let the vertices of the rectangle be $A(2, -2)$,$B(8, 4)$,$C(5, 7)$,and $D(x, y)$.Since the diagonals of a rectangle bisect each other,the midpoint of diagonal $AC$ is the same as the midpoint of diagonal $BD$.Midpoint of $AC = (\frac{2 + 5}{2}, \frac{-2 + 7}{2}) = (3.5, 2.5)$.Midpoint of $BD = (\frac{8 + x}{2}, \frac{4 + y}{2})$.Equating the midpoints:$\frac{8 + x}{2} = 3.5$ $\Rightarrow 8 + x = 7$ $\Rightarrow x = -1$.$\frac{4 + y}{2} = 2.5$ $\Rightarrow 4 + y = 5$ $\Rightarrow y = 1$.Thus,the fourth vertex is $(-1, 1)$.

If the three vertices of a rectangle taken in order are the points $(2, -2)$,$(8, 4)$,and $(5, 7)$,then the coordinates of the fourth vertex are:

Similar Questions

The triangle formed by joining the points $P(2, 7)$,$Q(4, -1)$,and $R(-2, 6)$ is:

Let $ABCD$ be a trapezium,in which $AB$ is parallel to $CD$,$AB=11$,$BC=4$,$CD=6$ and $DA=3$. The distance between $AB$ and $CD$ is

$\Delta ABC$ has integral side lengths. The internal angle bisector of angle $B$ meets side $AC$ at $D$. If $AD = 3$ and $DC = 8$,then the perimeter of $\Delta ABC$ is:

The points $(-a,-b), (a, b), (0,0)$ and $(a^{2}, ab)$ where $a \neq 0, b \neq 0$ are always

Let $(\alpha, \beta)$ be the centroid of the triangle formed by the lines $15x - y = 82$,$6x - 5y = -4$,and $9x + 4y = 17$. Then $\alpha + 2\beta$ and $2\alpha - \beta$ are the roots of the equation $...........$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module