Question
Find the area of $\triangle\text{ABC}$ whose vertices are:
$A(3, 8), B(-4, 2)$ and $C(5, -1)$
$A(3, 8), B(-4, 2)$ and $C(5, -1)$
✓
Answer
$A(3, 8), B(-4, 2)$ and $C(5, -1$) are the vertices of $\triangle\text{ABC}.$
Then, $(x_1 = 3, y_1= 8), (x_2 = -4, y_2 = 2)$ and $(x_3 = 5, y_3 = -1)$
Area of triangle ABC
$=\frac{1}{2}\big\{\text{x}_1(\text{y}_2-\text{y}_3)+\text{x}_2(\text{y}_3-\text{y}_1)+\text{x}_3(\text{y}_1-\text{y}_2)\big\}$
$=\frac{1}{2}\big\{3(2-(-1))+(-4)(-1-8)+5(8-2)\big\}$
$=\frac{1}{2}\big\{3(2+1)-4(-9)+5(6)\big\}$
$=\frac{1}{2}\big\{9+36+30\big\}$
$=\frac{1}{2}(75)$
$=37.5\ \text{sq}.\text{units}$
Then, $(x_1 = 3, y_1= 8), (x_2 = -4, y_2 = 2)$ and $(x_3 = 5, y_3 = -1)$
Area of triangle ABC
$=\frac{1}{2}\big\{\text{x}_1(\text{y}_2-\text{y}_3)+\text{x}_2(\text{y}_3-\text{y}_1)+\text{x}_3(\text{y}_1-\text{y}_2)\big\}$
$=\frac{1}{2}\big\{3(2-(-1))+(-4)(-1-8)+5(8-2)\big\}$
$=\frac{1}{2}\big\{3(2+1)-4(-9)+5(6)\big\}$
$=\frac{1}{2}\big\{9+36+30\big\}$
$=\frac{1}{2}(75)$
$=37.5\ \text{sq}.\text{units}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In the given figure, LM = LN = 46°. Express x in terms of a, b and c where a, b, c are lengths of LM, MN and NK respectively.
$\sqrt{\frac{1+\sin\text{A}}{1-\sin\text{A}}}=\sec\text{A}+\tan\text{A}$
→Write the standard form of a quadratic polynomial with real coefficients.
Find the depth of a cylindrical tank of radius 28m, if its capacity is equal to that of a rectangular tank of size 28m × 16m × 11m.
Find the common difference of the $A.P$. and write the next two terms:
$1.8, 2.0, 2.2, 2.4, .....$
→$1.8, 2.0, 2.2, 2.4, .....$
Write first four terms of the AP, when the first term a = 10 and the common difference d = 10.
A ladder 15m long just reaches the top of a vertical wall. If the ladders makes an angle of 60° with the wall, then find the height of the wall.
Write the condition of collinearity of points $\left(x_1, y_1\right),\left(x_2, y_2\right)$ and $\left(x_3, y_3\right)$.
→The graph of the polynomial $f(x) = ax^2 + bx + c$ is as shown below Fig. Write the signs of 'a' and $b^2 - 4ac.$
→A jar contains 54 marbles, each of which some are blue, some are green and some are white. The probabiliy of selecting a blue marble at random is $\frac{1}{3}$ and the probability of selecting a green marble at random is $\frac{4}{9}.$ How many white marbles does the jar contain?
→