What is the ratio of the area of triangle PQS | vedclass

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

Question

(C) The coordinates of $P$ and $Q$ are $(1, 2\sqrt{2})$ and $(1, -2\sqrt{2})$.The length of the base $PQ$ is $|2\sqrt{2} - (-2\sqrt{2})| = 4\sqrt{2}$.

Vedclass · Accepted Answer

$1 : 4$

Vedclass · Answer

(C) The coordinates of $P$ and $Q$ are $(1, 2\sqrt{2})$ and $(1, -2\sqrt{2})$.The length of the base $PQ$ is $|2\sqrt{2} - (-2\sqrt{2})| = 4\sqrt{2}$.Assuming the vertices $R$ and $S$ have $x$-coordinates such that the heights are $8$ and $2$ respectively:Area of $	riangle PQR = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes 4\sqrt{2} 	imes 8 = 16\sqrt{2}$.Area of $	riangle PQS = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes 4\sqrt{2} 	imes 2 = 4\sqrt{2}$.The ratio of the area of $	riangle PQS$ to the area of $	riangle PQR$ is $\frac{4\sqrt{2}}{16\sqrt{2}} = \frac{1}{4}$,which is $1 : 4$.

What is the ratio of the area of $\triangle PQS$ to the area of $\triangle PQR$?

Similar Questions

If the lines $x + 3y = 4$ and $6x - 2y = 7$ are the diagonals of a parallelogram $PQRS$,then $PQRS$ is a:

The triangle with vertices $A(2, 4)$,$B(2, 6)$,and $C(2 + \sqrt{3}, 5)$ is a . . . .

The three points $(-2, 2)$,$(8, -2)$,and $(-4, -3)$ are the vertices of:

The sides of a triangle are $3x+2y-6=0$,$2x-3y+6=0$,and $x+2y+2=0$. If $P(0, b)$ lies either on the triangle or inside the triangle,then $b$ lies in the interval

Suppose $\triangle ABC$ is an isosceles triangle with $\angle C=90^{\circ}$,$A=(2,3)$ and $B=(4,5)$. Then the centroid of the triangle is

Vedclass Test Series

Exam Paper Generator

Online Exam Module