MCQ
Consider a $\triangle A B C$ in the $X Y$-plane with vertices $A=(0,0), B=(1,1)$ and $C=(9,1)$. If the line $x=a$ divides the triangle into two parts of equal area, then a equals
- ✓$3$
- B$3.5$
- C$4$
- D$4.5$
✓
Answer
Correct option: A.
$3$
a
(a)
(a)
Given, in $\triangle A B C$
$A(0,0), B(1,1) C(9,1)$
$\text { Area of } \triangle C D E=\frac{1}{2} \text { Area of } \triangle A B C$ $\Rightarrow \quad \frac{1}{2} \times C D \times D E=\frac{1}{4} \times B C \times A P$ $\Rightarrow \quad \frac{1}{2}(9-a) \times\left(1-\frac{a}{9}\right)=\frac{1}{4} \times 8 \times 1$
$\Rightarrow \quad (9-a)(9-a)=36$
$\Rightarrow \quad 9-a=6 \Rightarrow a=3$
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
An urn contains marbles of four colours : red, white, blue and green. When four marbles are drawn without replacement, the following events are equally likely
→$1.$ the selection of four red marbles.
$2.$ the selection of one white and three red marbles.
$3.$ the selection of one white, one blue and two red marbles.
$4.$ the selection of one marble of each colour.
The smallest total number of marbles satisfying the given condition is
The polynomial equation $x^3-3 a x^2+\left(27 a^2+9\right) x+2016=0$ has
→If the arcs of the same length in two circles $S_1$ and $S_2$ subtend angles $75^o $ and $120^o $ respectively at the centre. The ratio $\frac{{{S_1}}}{{{S_2}}}$ is equal to
→Solve $2\text{x}^2+\text{x}+1=0$.
→The ratio in which yz-plane divides the line segment joining (-3, 4, 2), (2, 1, 3) is:
The eccentricity of the hyperbola $5{x^2} - 4{y^2} + 20x + 8y = 4$ is
→Let $x$ and $y$ be distinct integers where $1 \leq x \leq 25$ and $1 \leq y \leq 25$. Then, the number of ways of choosing $x$ and $y$, such that $x + y$ is divisible by $5$ , is $.........$.
→The number $111......1 $ ( $ 91$ times) is
→Let $A$ and $B$ be two sets then $(A \cup B)' \cup (A' \cap B)$ is equal to
→Let $R$ be a relation from the set $\{1,2,3 \ldots \ldots \ldots, 60\}$ to itself such that $R =\{( a , b ): b = pq$, where $p , q \geq 3$ are prime numbers $\}$. Then, the number of elements in $R$ is.
→