The points A(2, 1),B(3, -2) and C(a, b) are v | vedclass

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

Question

(B) Given,$ABCD$ is a rectangle. Slope of $AB = \frac{-2-1}{3-2} = -3 = m_1$. Since $AB \perp BC$,the slope of $BC$ is $m_2 = -\frac{1}{m_1} = \frac{1

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(B) Given,$ABCD$ is a rectangle. Slope of $AB = \frac{-2-1}{3-2} = -3 = m_1$. Since $AB \perp BC$,the slope of $BC$ is $m_2 = -\frac{1}{m_1} = \frac{1}{3}$. Slope of $BC = \frac{b - (-2)}{a - 3} = \frac{b+2}{a-3} = \frac{1}{3}$. $3(b+2) = a-3$ $\Rightarrow 3b + 6 = a - 3$ $\Rightarrow a - 3b = 9$ ... $(i)$. Since $CD \parallel AB$,the slope of $CD$ is $m_3 = m_1 = -3$. The points $C(a, b)$ and $P(3, 4)$ lie on the line $CD$. Slope of $CP = \frac{4-b}{3-a} = -3$. $4-b = -3(3-a)$ $\Rightarrow 4-b = -9 + 3a$ $\Rightarrow 3a + b = 13$ ... $(ii)$. Multiplying $(ii)$ by $3$: $9a + 3b = 39$ ... $(iii)$. Adding $(i)$ and $(iii)$: $(a - 3b) + (9a + 3b) = 9 + 39$ $\Rightarrow 10a = 48$ $\Rightarrow a = 4.8 = \frac{24}{5}$. Substituting $a = 4.8$ in $(ii)$: $3(4.8) + b = 13$ $\Rightarrow 14.4 + b = 13$ $\Rightarrow b = -1.4 = -\frac{7}{5}$. Now,$5a + 10b = 5(\frac{24}{5}) + 10(-\frac{7}{5}) = 24 - 14 = 10$.

The points $A(2, 1)$,$B(3, -2)$ and $C(a, b)$ are vertices of the rectangle $ABCD$. If the point $P(3, 4)$ lies on the line $CD$,then $5a + 10b = $

Similar Questions

Find the area of the triangle formed by the lines $y-x=0$,$x+y=0$,and $x-k=0$.

For a right-angled triangle having the lengths of two sides as $2 \sqrt{2}$ and $5$,find the possible lengths of the third side.

The diagonal passing through the origin of a quadrilateral formed by $x = 0, y = 0, x + y = 1$ and $6x + y = 3$ is

The coordinates of three points $A(-4, 0)$,$B(2, 1)$,and $C(3, 1)$ determine the vertices of an isosceles trapezium $ABCD$. The coordinates of the vertex $D$ are:

The area of the parallelogram formed by the lines $y = mx, y = mx + 1, y = nx, y = nx + 1$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module