Question
Find the distance between the points $P(-1,1)$ and $Q(5,-7)$.
✓
Answer
Suppose co-ordinates of point $\mathrm{P}$ are $\left(x_1, y_1\right)$ and of point $\mathrm{Q}$ are $\left(x_2, y_2\right)$.
$
x_1=-1, \quad y_1=1, \quad x_2=5, \quad y_2=-7
$
According to distance formula, $\mathrm{d}(\mathrm{P}, \mathrm{Q})=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$
$
\begin{aligned}
& =\sqrt{[5-(-1)]^2+[(-7)-1]^2} \\
& =\sqrt{(6)^2+(-8)^2} \\
& =\sqrt{36+64} \\
d(P, Q) & =\sqrt{100}=10
\end{aligned}
$
$\therefore$ distance between points $\mathrm{P}$ and $\mathrm{Q}$ is 10 .
$
x_1=-1, \quad y_1=1, \quad x_2=5, \quad y_2=-7
$
According to distance formula, $\mathrm{d}(\mathrm{P}, \mathrm{Q})=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$
$
\begin{aligned}
& =\sqrt{[5-(-1)]^2+[(-7)-1]^2} \\
& =\sqrt{(6)^2+(-8)^2} \\
& =\sqrt{36+64} \\
d(P, Q) & =\sqrt{100}=10
\end{aligned}
$
$\therefore$ distance between points $\mathrm{P}$ and $\mathrm{Q}$ is 10 .
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
If one zero of the polynomial $(a^2 + 9)x^2 + 13x + 6a$ is the reciprocal of the other, find the value of $a$.
→Three cubes of iron whose edges are $6\ cm, 8\ cm$ and $10\ cm$, respectively are melted and formed into a single cube. Find the edge of the new cube formed.
→The areas of two circles are in th ratio $4 : 9$. What is the ratio between their circumferences?
→Write an A.P. whose first term is a and common difference is d in each of the following.
$a=-7, d=\frac{1}{2}$
→$a=-7, d=\frac{1}{2}$
Find the correct answer from the alternatives given.The median of the distances covered per litre shown in the above data is in the group $. . . . .$
→ Solve the following simultaneous equation.
x + 7y = 10; 3x – 2y = 7
x + 7y = 10; 3x – 2y = 7
$\triangle\text{ABD}$ is a right triangle right-angled at A and $\text{AC}\perp\text{BD}.$ Show that
$\frac{\text{AB}^2}{\text{AC}^2}=\frac{\text{BD}}{\text{DC}}$
→$\frac{\text{AB}^2}{\text{AC}^2}=\frac{\text{BD}}{\text{DC}}$
In the given figure, a circle with centre O, is inscribed in a quadrilateral ABCD such that it touches the side BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29cm, AD = 23cm, $\angle\text{B} = 90^\circ$and DS = 5cm then find the radius of the circle.
→Find $n$, if the $n^{\text {th }}$ term of the following sequence is 68 .
$5,8,11,14, \ldots$
→$5,8,11,14, \ldots$
In ΔPQR, point S is the midpoint of side QR. If PQ = 11,PR = 17, PS = 13,find QR.