How Far is the Point (–3, –4) From the Origin? GMAT Problem Solving

Question: How far is the point (–3, –4) from the origin?

1. 2
2. 2.5
3. 5
4. \(4\sqrt2\)
5. \(4\sqrt3\)

Correct Answer: C

Solution and Explanation
Approach Solution 1:

Signs can be ignored and only magnitudes can be considered because we have to find the distance.

As a result, on the X-axis, (-3) will represent a distance of magnitude 3 from the origin.

On the Y-axis, (-4) will represent a distance of magnitude 4 from the origin.

As a result, the distance from the origin will be equal to the diagonal of the rectangle created by one of its edges being at the origin and the other at point (-3,-4).
The Pythagoras theorem can also be used to determine the diagonal (similar to finding the hypotenuse of a right-angled triangle).

Distance =\(\sqrt{(3^2+4^2)}\)

Hence the distance of point ( -3,- 4) from origin is 5 units.
The correct option is C which is 5

Approach Solution 2:

Lets approach this problem with the distance formula :

Point of origin = \([x_1 , y_1]\) = [0 , 0]

Another point =\([x_2 , y_2]\) = [-3 , 4]

to find the distance between the given points let us use the distance formula :
Here D signifies distance

D = \(\sqrt{[x^2-x^1]^2-[y^2-y^1]^2}\)

D =\(\sqrt{[-3-0]^2-[-4-0]^2}\)

D = \(\sqrt{9-16}\)

D = \(\sqrt{25}\)

Square root of 25 is 5
Therefore, D = 5
Hence the distance of point ( -3,- 4) from origin is 5 units.
The correct option is C , which is 5

Approach Solution 3:
Point of origin = 

Another point  = 

So, to find the distance between the given points we will use distance formula :

Substitute the given values .

Hence the distance of point ( -3, 4) from origin is 5 units.

“How far is the point (–3, –4) from the origin?”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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