The area of a triangle is 5 and two of its ve | vedclass

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

Question

(A) Let the third vertex be $C(h, k)$.Since $C$ lies on the line $y = x + 3$,we have $k = h + 3$  .........$(1)$The area of the triangle with vertices

Vedclass · Accepted Answer

$\left( \frac{7}{2}, \frac{13}{2} \right)$

Vedclass · Answer

(A) Let the third vertex be $C(h, k)$.Since $C$ lies on the line $y = x + 3$,we have $k = h + 3$  .........$(1)$The area of the triangle with vertices $(h, k), (2, 1), (3, -2)$ is given by:$\frac{1}{2} |h(1 - (-2)) + 2(-2 - k) + 3(k - 1)| = 5$$|h(3) + 2(-2 - k) + 3(k - 1)| = 10$$|3h - 4 - 2k + 3k - 3| = 10$$|3h + k - 7| = 10$Case $1$: $3h + k - 7 = 10 \implies 3h + k = 17$  .........$(2)$Substitute $k = h + 3$ into $(2)$:$3h + (h + 3) = 17 \implies 4h = 14 \implies h = \frac{7}{2}$Then $k = \frac{7}{2} + 3 = \frac{13}{2}$. So,$C = \left( \frac{7}{2}, \frac{13}{2} \right)$.Case $2$: $3h + k - 7 = -10 \implies 3h + k = -3$  .........$(3)$Substitute $k = h + 3$ into $(3)$:$3h + (h + 3) = -3 \implies 4h = -6 \implies h = -\frac{3}{2}$Then $k = -\frac{3}{2} + 3 = \frac{3}{2}$. So,$C = \left( -\frac{3}{2}, \frac{3}{2} \right)$.

The area of a triangle is $5$ and two of its vertices are $A(2, 1)$ and $B(3, -2)$. The third vertex,which lies on the line $y = x + 3$,is:

Similar Questions

Two sides of a rhombus are along the lines $x-y+1=0$ and $7x-y-5=0$. If its diagonals intersect at $(-1,-2)$,then one of the vertices of this rhombus is

The diagonals of the parallelogram whose sides are $lx + my + n = 0$,$lx + my + n' = 0$,$mx + ly + n = 0$,and $mx + ly + n' = 0$ include an angle of:

The sides of a triangle are $3x + 4y$,$4x + 3y$,and $5x + 5y$ units,where $x, y > 0$. The triangle is:

If the vertices of a triangle $ABC$ are $A(1,7)$,$B(-5,-1)$,and $C(7,4)$,then the equation of the internal angle bisector of $\angle ABC$ is

When are the points with coordinates $(2a, 3a)$,$(3b, 2b)$,and $(c, c)$ collinear?

Vedclass Test Series

Exam Paper Generator

Online Exam Module