Question

Need Help ASAP it's due today. Angelica uses the point (4,3) to represent the location of her house and uses the point (10,8) to represent the location of a gas station. Each unit on the graph represents 1 mi. How far is the gas station from Angelica's house? SHOW YOUR WORK. ( The teacher said to Plot a third point, connect the third point to make a right triangle, find the lengths of the legs of the triangle and then use the pythagorean theorem to find the distance between the gas station and Angelica's house). ​Only answer if you truly know how to solve this please. Will Mark Brainliest

Answer 1

Answer:

About 7.8 miles.

Step-by-step explanation:

We can use the distance formula to find the distance from the gas station to the house.

However, your teacher said to use the Pythagorean Theorem to find the distance.

Going by your teacher's preferred method:

(4,3), (10,8), and (10,3) would make a right triangle.

[See Picture]

Angelica's house is at point (4,3). It is 6 units from our new third point.

The gas station is at point (10,8). It is 5 units form out new third point.

The legs are 5 and 6 units. The distance from the house to the gas station would be our hypotenuse.

Use the Pythagorean Theorem to find the length of the hypotenuse.

$a^2 + b^2 = c^2\\\\\text {Replace a and b with the appropriate values: }\\6^2 + 5^2 = c^2\\\text {Solve: }\\6^2 + 5^2 = c^2\\6^2 = 36\\5^2 = 25\\\rightarrow 36 + 25 =c^2\\36 + 25 = 61\\\rightarrow 61=c^2\\\sqrt{61}=\sqrt{c} \\\boxed {7.81024967591=c}$

7.81024967591 ≈ 7.8

The hypotenuse is about 7.8.

Therefore, the distance between the gas station and Angelica's house should be about 7.8 miles.

Brainilest Appreciated!

Answer 2

Answer:

AG = 7,8

Step-by-step explanation:

Plot the third point at (10,3) and let's call it point B.

Now construct the right sided triangle A B G

With A = (4,3) , B = (10,3) and G = (10,8).

AB is horizontal so subtract the x coordinates of point A and point B. So AB has length 10 - 4 = 6

BG is vertical so subtract the y coordinates of point B and point G. So BG has length 8 - 3 = 5

Now use pythagorean theorem to calculate AG

In any right sided triangle you can use a² + b² = c²

In our case AB² + BG² = AG²

Substitute AB = 6 and BG = 5

6² + 5² = AG²

AG² = 6*6 + 5*5

AG² = 36 + 25

AG = + - SQRT(61)

{Only the + variant of the SQRT has a meaning here.}

AG = 7,81 rounded on one decimal AG = 7,8