Question
If the points $\mathrm{A}(h, 0), \mathrm{B}(0, \mathrm{k})$ and $\mathrm{C}(\mathrm{a}, \mathrm{b})$ lie on a line, then show that $\frac{a}{h}+\frac{b}{k}=1$.'
✓
Answer
Given, A(h, 0), B(0, k) and C(a, b) Since the points A, B and C lie on a line, they are collinear. ∴ Slope of AB = slope of BC
$\begin{array}{ll}\therefore \quad & \frac{k-0}{0-h}=\frac{b-k}{a-0} \\ \therefore \quad & a k=-h(b-k) \\ \therefore \quad & \frac{a}{h}=\frac{k-b}{k} \\ \therefore \quad & \frac{a}{h}=1-\frac{b}{k} \\ \therefore \quad & \frac{a}{h}+\frac{b}{k}=1\end{array}$
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
Prove the following : $\frac{\cos 15^{\circ}-\sin 15^{\circ}}{\cos 15^{\circ}+\sin 15^{\circ}}=\frac{1}{\sqrt{3}}$
→Prove that the lines $2x + 3y = 19$ and $2x + 3y + 7 = 0$ are equidistant from the line $2x + 3y = 6$.
→$\sec \theta=-3$ and $\pi<\theta<\frac{3 \pi}{2}$ then find the values of other trigonometric functions.
→The mean and standard deviations of the two brands of watches are given below:
Calculate the coefficient of variation of the two brands and interpret the results.
Construct a matrix $A=\left[a_{i j}\right]_{3 \times 2}$ whose elements ay are given by
→$a_{i j}=\frac{(i-j)^2}{5-i}$
If $p, q, r, s$ are in G.P., show that $\left(p^2+q^2+r^2\right)\left(q^2+r^2+s^2\right)=(p q+q r+r s)^2$.
→$\sqrt{ } 3 \operatorname{cosec} 20^{\circ}-\sec 20^{\circ}=4$
→Verify that $f$ and $g$ are inverse functions of each other, where
→$\mathrm{f}(\mathrm{x})=\frac{x-7}{4}, \mathrm{~g}(\mathrm{x})=4 \mathrm{x}+7$
Find $\lim\limits_{\text{x}\rightarrow1}\text{f(x)}$ if $\text{f(x)}=\begin{cases}\text{x}^2-1, & \text{x} \le1\\-\text{x}^2-1, &\text{x} > 1\end{cases}.$
→Find the co-ordinates of a point of the parabola $y^2 = 8x$ having focal distance $10.$
→