Question

How far from the origin is the point (-5, -12)?

Answer 1

The first question is (7)

Answer 2

Answer:

13 units

Perimeter is 11.31 units

Step-by-step explanation:

To find the distance between two points, we use the distance formula

$d=\sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }$.  

Chose a point to be $(x_1,y_1)$ and another point to be $(x_2,y_2)$.

Let the origin (0,0) be $(x_1,y_1)$ where $x_1=0\\y_1=0$.

Let (-5,-12) be $(x_2,y_2)$ where $x_2=-5\\y_2=-12$.

Substitute the values.

$d=\sqrt{((-12-0)^{2}+(-5-0)^{2} }\\d=\sqrt{((-12)^{2}+(-5)^{2} }\\d=\sqrt{144+25}=\sqrt{169} =13$

The perimeter is found by finding the distance of each side and adding it together. Since it has all equal sides, it will be the same distance for all sides. We will find the distance of just one side from point D to A.

Let the point D the origin (0,0) be $(x_1,y_1)$ where $x_1=0\\y_1=0$.

Let the point A (2,2) be $(x_2,y_2)$ where $x_2=2\\y_2=2$.

Substitute the values.

$d=\sqrt{((2-0)^{2}+(2-0)^{2} }\\d=\sqrt{(2)^{2}+(2)^{2} }\\d=\sqrt{4+4}=\sqrt{8} =2.83$

Perimeter = 2.83+2.83+2.83+2.83= 11.31 units