Coordinate Geometry Question

Question

The points A(3, −5) and H(9, −3) are the endpoints of the line segment AH.

The point D is the midpoint of the line segment AH.

Find the length of AD.

Give your answer correct to 3 significant figures.

Answer 1

For this problem we will need the midpoint and distance formulas.

Since D is the given midpoint of segment AH, we need to find the midpoint of AH.

Midpoint Formula:

((x₁+x₂)/2 , ((y₁+y₂)/2)

Plugging in the values we get

((3+9)/2 , (-5+-3)/2)

((12/2), (-8/2))

(6,-4) This is our midpoint of AH or also known as point D

Next to find the distance of segment AD, we use the distance formula for AD

Distance Formula:

((x₂-x₁)²+(y₂-y₁)²)^1/2

*Note that raising this expression to the 1/2 power is the same as saying the square root of it.

Now plug in the values:

((6-3)²+(-4-5)²)^1/2

((3)²+(-9)²)^1/2

(9+81)^1/2

(90)^1/2

Now we know that the Distance of segment AD is (90)^1/2

With 3 significant digits it is 9.49