Question

1. in the cartesian plane, what is the distance of the point (2, -3) from the origin?

a) √5
b) √13
c) 5
d) 13

Explanation:

Step1: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, the origin is \((0,0)\) and the point is \((2,-3)\).

Step2: Substitute the values into the formula

Substitute \(x_1 = 0,y_1 = 0,x_2=2,y_2 = - 3\) into the formula. Then \(d=\sqrt{(2 - 0)^2+(-3 - 0)^2}\).

Step3: Simplify the expression

First, calculate \((2 - 0)^2=4\) and \((-3 - 0)^2 = 9\). Then \(d=\sqrt{4 + 9}=\sqrt{13}\).

Answer:

B. \(\sqrt{13}\)