Two vertices of a triangle are (0, 2) and (4, | vedclass

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

Question

(B) Let the third vertex be $A(h, k)$. Let the other two vertices be $B(0, 2)$ and $C(4, 3)$. The orthocenter $H$ is at $(0, 0)$.Since $AH \perp BC$,t

Vedclass · Accepted Answer

Second

Vedclass · Answer

(B) Let the third vertex be $A(h, k)$. Let the other two vertices be $B(0, 2)$ and $C(4, 3)$. The orthocenter $H$ is at $(0, 0)$.Since $AH \perp BC$,the slope of $AH 	imes$ slope of $BC = -1$.Slope of $BC = \frac{3 - 2}{4 - 0} = \frac{1}{4}$.Slope of $AH = \frac{k - 0}{h - 0} = \frac{k}{h}$.Therefore,$\frac{k}{h} 	imes \frac{1}{4} = -1 \implies k = -4h$.Since $BH \perp AC$,the slope of $BH 	imes$ slope of $AC = -1$.Slope of $AC = \frac{k - 3}{h - 4}$.Slope of $BH = \frac{2 - 0}{0 - 0}$ is undefined (vertical line $x = 0$).Thus,$AC$ must be a horizontal line,so $k = 3$.Substituting $k = 3$ into $k = -4h$,we get $3 = -4h$,so $h = -\frac{3}{4}$.The third vertex is $(-\frac{3}{4}, 3)$,which lies in the second quadrant.

Two vertices of a triangle are $(0, 2)$ and $(4, 3)$. If its orthocenter is at the origin $(0, 0)$,then its third vertex lies in which quadrant?

Similar Questions

If the vertices $P, Q, R$ of a triangle $PQR$ are rational points (points with rational coordinates),which of the following points is/are not necessarily a rational point?

The coordinates of the orthocentre of the triangle bounded by the lines $4x - 7y + 10 = 0$,$x + y = 5$,and $7x + 4y = 15$ are:

If $A(4, -3)$,$B(3, -2)$,and $C(2, 8)$ are the vertices of a triangle,what is the distance of its centroid from the $y$-axis?

If the line $bx + ay = 3ab$ intersects the coordinate axes at points $A$ and $B$,then the centroid of $\Delta OAB$ is:

Let $PS$ be the median of the triangle with vertices $P(2,2)$,$Q(6,-1)$,and $R(7,3)$. The equation of the line passing through $(1,-1)$ and parallel to $PS$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module