# Find the distance of each of the following points from the origin:

Question:

Find the distance of each of the following points from the origin:

(i) A(5, −12)
(ii) B(−5, 5)
(iii) C(−, −6)4

Solution:

(i) A(5, −12)
Let O(0, 0) be the origin.

$O A=\sqrt{(5-0)^{2}+(-12-0)^{2}}$

$=\sqrt{(5)^{2}+(-12)^{2}}$

$=\sqrt{25+144}$

$=\sqrt{169}$

$=13$ units

(ii) B(−5, 5)
Let O(0, 0) be the origin.

$O B=\sqrt{(-5-0)^{2}+(5-0)^{2}}$

$=\sqrt{(-5)^{2}+(5)^{2}}$

$=\sqrt{25+25}$

$=\sqrt{50}$

$=\sqrt{25 \times 2}$

$=5 \sqrt{2}$ units

(iii) C(−4, −6)
Let O(0,0) be the origin.

$O C=\sqrt{(-4-0)^{2}+(-6-0)^{2}}$

$=\sqrt{(-4)^{2}+(-6)^{2}}$

$=\sqrt{16+36}$

$=\sqrt{52}$

$=\sqrt{4 \times 13}$

$=2 \sqrt{13}$ units