Question

Point 'p' trisects the line segment joining the points (5, 7) and (2, 4) then its distance from origin may be equal to

Answer 1

$2\sqrt{13}$ units or $\sqrt{34}$ units

Given data:

P trisects the line segment joining the points (5, 7) and (2, 4)

To find:

Distance of P from origin

Step-by-step explanation:

Case 1.

Since P trisects the line segment joining the points (5, 7) and (2, 4), P divides the line segment into the ratio 1 : 2.

So, the coordinates of P are

$(\dfrac{5\times 2+2\times 1}{1+2},\dfrac{7\times 2+4\times 1}{1+2})$

i.e., (4, 6)

Now the distance of P (4, 6) from origin O (0, 0) is

$d_{1}=\sqrt{4^{2}+6^{2}}$ units

= $\sqrt{52}$ units

= $2\sqrt{13}$ units

Case 2.

Since P trisects the line segment joining the points (5, 7) and (2, 4), P divides the line segment into the ratio 2 : 1.

So, the coordinates of P are

$(\dfrac{5\times 1+2\times 2}{2+1},\dfrac{7\times 1+4\times 2}{2+1})$

i.e., (3, 5)

Now the distance of P (3, 5) from origin O (0, 0) is

$d_{2}=\sqrt{3^{2}+5^{2}}$ units

= $\sqrt{34}$ units

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