Question

Camp Sunshine is also on the lake. Use the

Pythagorean Theorem to find the distance
between Francesca's house and Camp
Sunshine to the nearest tenth of a meter.​

Answer 1

Answer: The distance is 214.7 meters

Step-by-step explanation: Please refer to the picture attached for details.

The coordinates given shows that Francesca's house lies at the point (10,20) and the distance to the right is also at the point (200,20), and this point which we shall call B is actually measuring 190 meters. Francesca's house at point H is located at 10 units on the x-axis, while point B is located at 200 units on the x-axis. Hence the actual measurement is 200 - 10 which equals 190 units (or 190 meters).

Similarly, Camp Sunshine or point C lies on (200,120) which makes it located at 120 units on the y-axis, and point B which lies on (200,20) is located at 20 units on the y-axis. This makes the distance from point B to point C measure as 120 - 20 which equals 100 units.

Using the Pythagoras' theorem, which states that AC² = AB² +BC², where AC is the hypotenuse (longest side),

The distance from her house to camp sunshine is given as

HC² = HB² + CB²

HC² = 190² + 100²

HC² = 36100 + 10000

HC² = 46100

Add the square root sign to both sides of the equation

√HC² = √46100

HC = 214.7091

HC ≈ 214.7 (to the nearest tenth of a meter)

Therefore the distance between Francesca's house to camp sunshine is 214.7 meters

Answer 2

the distance between Francesca's house and Camp Sunshine is 214.7 units

Explanation:

Given

• the coordinates of the house is (10.20)
• the coordinates of the camp is (200, 120)
• the coordinates of the right angle point is (200, 20)

To find a distance between two points or the length of the segment, we use the following formula:

`√((x2-x1)^2+(y2-y1)^2)`

• the distance of the house to the right angle point is

=
`√((200-10)^2+(20-20)^2)` =
`\sqrt{190^(2) } =190` units

• the distance from the right angle point to the Camp is:

=
`√((200-200)^2+(20-120)^2) = \sqrt{-100^(2) } = 100`

Use the Pythagorean Theorem to find the distance between Francesca's house and Camp

=
`\sqrt{100^(2) + 190^(2) } = √(46100) = 214.7` units

So the distance between Francesca's house and Camp Sunshine is 214.7 units