Two lines are drawn through (3, 4),each of wh | vedclass

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

Question

(B) The slope of the line $x - y = 2$ is $m_1 = 1$. Let the slope of the required lines be $m$. The angle between the lines is $45^\circ$,so $	an 45^

Vedclass · Accepted Answer

$9/2$

Vedclass · Answer

(B) The slope of the line $x - y = 2$ is $m_1 = 1$. Let the slope of the required lines be $m$. The angle between the lines is $45^\circ$,so $	an 45^\circ = |\frac{m - 1}{1 + m(1)}|$.$1 = |\frac{m - 1}{m + 1}|$.This gives $m - 1 = m + 1$ (which is impossible) or $m - 1 = -(m + 1)$,which implies $2m = 0$,so $m = 0$. The other line must be perpendicular to $y = 4$ (since the angle is $45^\circ$),so $x = 3$.The lines are $y = 4$,$x = 3$,and $x - y = 2$.The intersection points are:$1$) $y = 4$ and $x = 3 \implies (3, 4)$.$2$) $y = 4$ and $x - y = 2 \implies x = 6 \implies (6, 4)$.$3$) $x = 3$ and $x - y = 2 \implies y = 1 \implies (3, 1)$.The area of the triangle with vertices $(3, 4), (6, 4), (3, 1)$ is $\frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes |6 - 3| 	imes |4 - 1| = \frac{1}{2} 	imes 3 	imes 3 = \frac{9}{2}$.

Two lines are drawn through $(3, 4)$,each of which makes an angle of $45^\circ$ with the line $x - y = 2$. The area of the triangle formed by these lines is:

Similar Questions

Let the midpoints of the sides of a triangle $ABC$ be $(\frac{5}{2}, 7)$, $(\frac{5}{2}, 3)$, and $(4, 5)$. If its incentre is $(h, k)$, then $3h + k$ is equal to:

If the points $(k, 3), (2, k),$ and $(-k, 3)$ are collinear,then the values of $k$ are

$A$ square is formed by the lines $x=0, y=0, x=1, y=1$. Then,the equations of its diagonals will be

In a $\triangle ABC$,$D$ and $E$ are points on $AB$ and $AC$ respectively such that $DE \parallel BC$. Suppose $BE$ and $CD$ intersect at $O$. If the areas of $\triangle ADE$ and $\triangle ODE$ are $3$ and $1$ respectively,find the area of $\triangle ABC$.

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module