Question

which is the best estimate of the distance between the point (-25, 10) and the origin? 15 units 23 units 8 units 27 units

Explanation:

Step1: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). The origin is \((0,0)\), and the given point is \((-25,10)\). So \(x_1=-25,y_1 = 10,x_2=0,y_2 = 0\).

Step2: Substitute values into the formula

Substitute into the formula: \(d=\sqrt{(0-(-25))^2+(0 - 10)^2}=\sqrt{25^2+(- 10)^2}=\sqrt{625 + 100}=\sqrt{725}\).

Step3: Estimate the value of \(\sqrt{725}\)

We know that \(27^2=729\) and \(26^2 = 676\). Since \(725\) is very close to \(729\).

Answer:

\(27\) units