Question

What is the length of segment RS

Answer 1

Answer: 13 units

Step-by-step explanation:

The length of line segment AB with points $A(x_1,y_1)\ and\ B(x_2,y_2)$ is given by distance formula as :

$\text{AB}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Now, the length of line segment RS with points $R(-4,-3)\ and\ S(1,9)$ is given by distance formula as :

$\text{RS}=\sqrt{(1-(-4))^2+(9-(-3))^2}\\\Rightarrow\ RS=\sqrt{(5)^2+(12)^2}\\\Rightarrow\ RS=\sqrt{25+144}=\sqrt{169}\\\Rightarrow\ RS=13$

Hence, the length of segment RS= 13 units

Answer 2

The length of segment RS must be 13 units.

To find this, you can make a right triangle by connecting points R and S at a common point to form a right angle. The segments made would be 5 units and 12 units long. Using the Pythagorean Theorem, the segment RS must be 13 units.