The circumcentre of a triangle formed by the | vedclass

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

Question

(A) The given equations are $xy + 2x + 2y + 4 = 0$ and $x + y + 2 = 0$.Factorizing the first equation: $x(y + 2) + 2(y + 2) = 0 \Rightarrow (x + 2)(y

Vedclass · Accepted Answer

$(-1, -1)$

Vedclass · Answer

(A) The given equations are $xy + 2x + 2y + 4 = 0$ and $x + y + 2 = 0$.Factorizing the first equation: $x(y + 2) + 2(y + 2) = 0 \Rightarrow (x + 2)(y + 2) = 0$.This represents two lines: $x = -2$ and $y = -2$.The second equation is $x + y + 2 = 0$.To find the vertices of the triangle,we find the intersection points of these lines:$1$. Intersection of $x = -2$ and $y = -2$ is $(-2, -2)$.$2$. Intersection of $x = -2$ and $x + y + 2 = 0$ is $(-2, 0)$.$3$. Intersection of $y = -2$ and $x + y + 2 = 0$ is $(0, -2)$.The vertices of the triangle are $A(-2, -2)$,$B(-2, 0)$,and $C(0, -2)$.This is a right-angled triangle with the right angle at vertex $A(-2, -2)$ because the lines $x = -2$ and $y = -2$ are perpendicular.In a right-angled triangle,the circumcentre is the midpoint of the hypotenuse $BC$.The hypotenuse connects $B(-2, 0)$ and $C(0, -2)$.Midpoint $= (\frac{-2 + 0}{2}, \frac{0 - 2}{2}) = (-1, -1)$.Thus,the circumcentre is $(-1, -1)$.

The circumcentre of a triangle formed by the lines $xy + 2x + 2y + 4 = 0$ and $x + y + 2 = 0$ is

Similar Questions

The orthocentre of the triangle formed by the lines $x + y = 1$,$2x + 3y = 6$,and $4x - y + 4 = 0$ lies in which quadrant?

Assertion: If $(0, 3), (1, 1)$ and $(-1, 2)$ are the midpoints of the sides of a triangle,then the centroid of the original triangle is $(0, 2)$.
Reason: The centroid of a triangle and the centroid of the triangle formed by joining the midpoints of the sides of the original triangle are the same.

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

Let $PQR$ be an acute-angled triangle in which $PQ < QR$. From the vertex $Q$,draw the altitude $QQ_1$,the angle bisector $QQ_2$,and the median $QQ_3$,with $Q_1, Q_2, Q_3$ lying on $PR$. Then,

If the midpoints of the sides of a triangle are $(0, 1)$,$(1, 1)$,and $(1, 0)$,find the $x$-coordinate of its incentre.

Vedclass Test Series

Exam Paper Generator

Online Exam Module