Question

What is the length of segment XY?​

Answer 1

Answer: Third option.

Step-by-step explanation:

You need to use the formula for calculate the distance between two points. This is:

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

You can observe in the graph that the coordinates of the point X and the point Y are the following:

X(-4,0) and Y(3,2)

Knowing this, you can substitute the coordinates into the formula.

You get that the lenght of the segment XY is:

 $d_{(XY)}=\sqrt{(3-(-4))^2+(2-0)^2}\\\\d_{(XY)}=\sqrt{53}\ units$

This matches with the third option.

Answer 2

Answer:

7.28 units to the nearest hundredth.

Step-by-step explanation:

Use the Pythagoras theorem.

If you examine the graph you see that the line segment is the hypotenuse of a right triangle with legs of length 2 and 7.

XY^2 = 2^2 + 7^2

XY^2 =  53

XY = √53

XY = 7.28.