Question
Find the distance between the points $\Big(\frac{-8}{5},2\Big)$ and $\Big(\frac{2}{5},2\Big).$
✓
Answer
The given points are $\text{A}\Big(\frac{-8}{5},2\Big)$ and $\text{B}\Big(\frac{2}{5},2\Big).$
Then, $\Big(\text{x}_1=\frac{-8}{5},\text{y}_1=2\Big)$ and $\Big(\text{x}_2=\frac{2}{5},\text{y}_2=2\Big)$
Therefore,
$\text{AB}=\sqrt{(\text{x}_2-\text{x}_1)^2+(\text{y}_2-\text{y}_1)^2}$
$=\sqrt{\Big\{\frac{2}{5}-\Big(\frac{-8}{5}\Big)\Big\}^2+(2-2)^2}$
$=\sqrt{(2)^2+(0)^2}=\sqrt{4+0}$
$=\sqrt{4}$
$=2\text{ units}$
Then, $\Big(\text{x}_1=\frac{-8}{5},\text{y}_1=2\Big)$ and $\Big(\text{x}_2=\frac{2}{5},\text{y}_2=2\Big)$
Therefore,
$\text{AB}=\sqrt{(\text{x}_2-\text{x}_1)^2+(\text{y}_2-\text{y}_1)^2}$
$=\sqrt{\Big\{\frac{2}{5}-\Big(\frac{-8}{5}\Big)\Big\}^2+(2-2)^2}$
$=\sqrt{(2)^2+(0)^2}=\sqrt{4+0}$
$=\sqrt{4}$
$=2\text{ units}$
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 adjoining figure, ABCD is a trapezium in which CD || AB and its digonals intersect at O. If AO = (2x + 1)cm, OC = (5x - 7)cm, DO = (7x - 5)cm and OB = (7x + 1)cm, find the value of x.
$\triangle PQR \sim \triangle ABC , PQ =3 cm, QR =4 cm, PR =5 cm$ $A (\triangle PQR ): A (\triangle ABC )=1: 4$. Construct both triangles
→The sum of squares of two consecutive natural numbers is 244; find the numbers.
Solve: $2^x+3^y=17,2^{x+2}-3^{y+1}=5$
→During a medical check-up, the number of heartbeats per minute of 30 patients were recorded and summarised as follows:
Mean, median, mode of grouped data, cumulative frequency graph and ogive.
Find the mean heartbeats per minute for these patients, choosing a suitable method.
| Number of heartbeats per minute | 65-68 | 68-71 | 71-74 | 74-77 | 77-80 | 80-83 | 83-86 |
| Number of patients | 2 | 4 | 3 | 8 | 7 | 4 | 2 |
Find the mean heartbeats per minute for these patients, choosing a suitable method.
A man arranges to pay off a debt of Rs 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of all debt unpaid, find the value of the first instalment.
Prove the following identities:
$\Bigg\{\frac{1}{\big(\sec^2\theta-\cos^2\theta\big)}+\frac{1}{\big(\text{cosec}^2\theta-\sin^2\theta\big)}\Bigg\}\big(\sin^2\theta\cos^2\theta\big)$
$=\frac{1-\sin^2\theta\cos^2\theta}{2+\sin^2\theta\cos^2\theta}$
→$\Bigg\{\frac{1}{\big(\sec^2\theta-\cos^2\theta\big)}+\frac{1}{\big(\text{cosec}^2\theta-\sin^2\theta\big)}\Bigg\}\big(\sin^2\theta\cos^2\theta\big)$
$=\frac{1-\sin^2\theta\cos^2\theta}{2+\sin^2\theta\cos^2\theta}$
Calculate the missing frequency from the following distribution, if the median of distribution is 24.
Age in years | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |
No. of persons | 5 | 25 |
| 18 | 7 |
The dimensions of a metallic cuboid are 44 cm x 42 cm x 21 cm. It is molten and recast into a sphere. Find the surface area of the sphere.
Show that the points (-3, -3), (3, 3) and $(-3\sqrt{3},3\sqrt{3})$ are the vertices of an equilateral triangle.
→