If three vertices of a square are (-4, 3),(10 | vedclass

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

Question

(B) Let the vertices of the square be $A(-4, 3)$,$B(10, 5)$,$C(12, -9)$,and $D(x, y)$.In a square,the diagonals bisect each other at the same midpoint

Vedclass · Accepted Answer

$(-2, -11)$

Vedclass · Answer

(B) Let the vertices of the square be $A(-4, 3)$,$B(10, 5)$,$C(12, -9)$,and $D(x, y)$.In a square,the diagonals bisect each other at the same midpoint.Let the diagonals be $AC$ and $BD$.The midpoint of $AC = ((-4 + 12)/2, (3 - 9)/2) = (8/2, -6/2) = (4, -3)$.The midpoint of $BD = ((10 + x)/2, (5 + y)/2)$.Equating the midpoints: $(10 + x)/2 = 4 \implies 10 + x = 8 \implies x = -2$.$(5 + y)/2 = -3 \implies 5 + y = -6 \implies y = -11$.Thus,the fourth vertex is $(-2, -11)$.

If three vertices of a square are $(-4, 3)$,$(10, 5)$,and $(12, -9)$,then find the fourth vertex of the square.

Similar Questions

If the midpoints of the sides $\overline{AB}$,$\overline{BC}$,and $\overline{CA}$ in $\Delta ABC$ are respectively $D(1, 2)$,$E(2, 1)$,and $F(3, 3)$,then find the centroid of $\Delta ABC$.

Find the area of the triangle whose vertices are $(-8, 4), (-6, 6)$ and $(-3, 9).$

The area of a triangle having vertices $A(3, 0)$,$B(0, 3)$,and $C(3, 3)$ is:

State whether the following statement is true or false. Justify your answer.
$A$ circle has its centre at the origin and a point $P(5,0)$ lies on it. The point $Q(6,8)$ lies outside the circle.

State whether the following statement is true or false. Justify your answer.
The points $A(-1, 0)$,$B(3, 1)$,$C(2, 2)$,and $D(-2, 1)$ are the vertices of a parallelogram.

Vedclass Test Series

Exam Paper Generator

Online Exam Module