The line joining $P (- 4, 5)$ and $Q (3, 2)$ intersects the $y -$ axis at point $R$ . $P M$ and $Q N$ are perpendicular from $P$ and $Q$ on the $x -$ axis.
Find :
the area of the quadrilateral $P M N Q$ .

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Solution

$\begin{matrix} s l o p e o f p q = \frac{5 - 2}{- 4 - 3} = \frac{- 3}{7} y - 2 = \frac{- 3}{7} (x - 3) 7 y - 14 = - 3 x + 9 7 y + 3 x = 23 a r e a o f P M N Q = \frac{1}{2} ∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} \begin{matrix} - 4 - 4 \end{matrix} 33 - 4 \end{matrix} \begin{matrix} \begin{matrix} 50 \end{matrix} 025 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣ = \frac{1}{2} (6 + 15 + 20 + 8) = \frac{34 + 15}{2} = \frac{49}{2} \end{matrix}$

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Similar questions

Q. the line segment joining P(-4,5) and Q(3,2) intersect the y- axis at R. PM and QN are perpendiculars from P and Q on the x axis.
find: 1) the ratio PR:QR
2) the cordinates of R
3) the area of the quadrilateral PMNQ

The line joining $P (- 4, 5)$ and $Q (3, 2)$ intersect the $y$ -axis at point $R$ . $P M$ and $Q N$ are perpendicular to $P$ and $Q$ on the $x$ - axis. Find:

(1) the ratio $P R : R Q$ .

(2) the coordinate of $R$ .

(3) the area of the quadrilateral $P M N Q$ .

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P (- 4, 5)

and

Q (3, 2)

intersects the

y -

axis at point

R

P M

and

Q N

are perpendicular from

P

and

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on the

x -

axis.
Find :
(i) the ratio

P R : R Q

The line joining P (–4, 4) & Q (3, 1), intersects the y – axis at R. PM & QN are the perpendiculars from P & Q to the – axis. Find

Q. In what ratio does the y-axis divide the line segment joining the point P(-4,5) and Q(3,-7)? Also, find the coordinates of the point of intersection.

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The line joining P(−4,5) and Q(3,2) intersects the y−axis at point R. PM and QN are perpendicular from P and Q on the x−axis. Find :the area of the quadrilateral PMNQ.

slopeofpq=5−2−4−3=−37y−2=−37(x−3)7y−14=−3x+97y+3x=23areaofPMNQ=12∣∣ ∣ ∣ ∣ ∣∣−4−433−450025∣∣ ∣ ∣ ∣ ∣∣=12(6+15+20+8)=34+152=492

The line joining $P (- 4, 5)$ and $Q (3, 2)$ intersects the $y -$ axis at point $R$ . $P M$ and $Q N$ are perpendicular from $P$ and $Q$ on the $x -$ axis.
Find :
the area of the quadrilateral $P M N Q$ .