Question

Use the Pythagorean Theorem to find the distance between points F and C.

A. 2 √3
B. √41
C. 4 √3
D. 3 √5

Answer 1

D. 3√5

Explanation:

The distance between points F and C is the hypotenuse of a right triangle. Therefore we can use Pythagoras Theorem to calculate the distance between these points.

From inspection of the given graph the coordinates of the two points are:

• Point C = (2, 2)
• Point F = (-4, -1)

The horizontal difference between the x-coordinates is:

`x_C-x_F=2-(-4)=6\; \sf units`

The vertical difference between the y-coordinates:

`y_C-y_F=2-(-1)=3\; \sf units`

Therefore, we have a right triangle with the following dimensions:

• Leg a = 3
• Leg b = 6
• Hypotenuse c = CF

`\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}`

To calculate the length of the hypotenuse, and therefore the distance between points C and F, substitute the values into the Pythagoras Theorem formula and solve for CF:

`\implies a^2+b^2=c^2`

`\implies 3^2+6^2=CF^2`

`\implies 9+36=CF^2`

`\implies CF^2=45`

`\implies √(CF^2)=√(45)`

`\implies CF=√(9 \cdot 5)`

`\implies CF=√(9) √(5)`

`\implies CF=3√(5)`

Therefore, the distance between points F and C is 3√5.