On the coordinate plane shown below, points g and i have coordinates (6,4) and (3,2), respectively.

a. design a strategy in which the pythagorean theorem is used to calculate the straight line distance between points g and i on a coordinate plane. use complete sentences to describe the strategy.

b. use the pythagorean theorem to determine the distance between the two points on the coordinate plane. in your final answer, include all of your calculations.

c. use the distance formula and the coordinates of points g and i to prove that the pythagorean theorem is an alternative method for calculating the distance between points on a coordinate plane. in your final answer, include all of your calculations.

Part A) see the procedure

Part B)

Part C)

Step-by-step explanation:

Part A) we know that

In a right triangle

The Pythagoras Theorem states that

where

c ----> is the hypotenuse of the right triangle

a,b -----> are the legs of the right triangle

In this problem

Let

a ------> the horizontal leg of the right triangle

b ------> the vertical leg of the right triangle

c-----> hypotenuse of the right triangle

so

Observing the graph

Part B) we know that

Applying the Pythagoras Theorem

we have

substitute the values

-----> hypotenuse IG

Part C) we have

The distance 's formula between two points is equal to

substitute the values

Therefore

The length side of the hypotenuse IG calculated with the Pythagoras theorem is equal to the distance obtained by the formula of distance between two points

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1