How to find the length of a line with distance formula - GRE Quantitative Reasoning

distance2 = (_x_2 – _x_1)2 + (_y_2 – _y_1)2

Looking at the two order pairs given, _x_1 = 1, _y_1 = 1, _x_2 = 7, _y_2 = 9.

distance2 = (7 – 1)2 + (9 – 1)2 = 62 + 82 = 100

distance = 10

distance2 = (_x_2 – _x_1)2 + (_y_2 – _y_1)2 + (_z_2 – _z_1)2

= (4 – 2)2 + (6 – 3)2 + (5 – 4)2

= 22 + 32 + 12

= 14

distance = √14

easiest way to do this is by plotting the points and turining it into a right triangle by using delta x and delta y

the delta x is 11-6 = 5

the delta y is 15-3 = 12

those form the two legs of the right triangle; the hypotenuse is the distance

dx2 +dy2= h2

25+144 = h2

169 = h2

h = 13

We can see that the distance between the two points in Quantity A is 4 because they have the same y-coordinate and x-coordinates that are 4 apart (10 – 6).

Quantity B is a little trickier to figure out and requires either the use of the formula below or creating a right triangle out of the two points.

Using the formula √\[(–2 – 1)2 + (4 – 1)2\] is √\[9 + 9\] which equals √18.

Although we don't know the square root of 18 automatically, we know that it will fall between √16 and √25 or 4 and 5. Since Quantity A is 4 and Quantity B has to be between 4 and 5, Quantity B is greater.

The man travels 40 meters north, 100 meters west, and 30 meters east. After he backtracks, he now has a cumulative distance west of 70 meters and he is 40 meters north. His wife has travelled east 60 meters and south 20 meters. Their positions can be modelled by the following points:

We can use the distance fomula to find the distance between the two points.

Half of this distance would be 71.59, approximately 72 meters.

distance2 = (_x_2 – _x_1)2 + (_y_2 – _y_1)2

Looking at the two order pairs given, _x_1 = 1, _y_1 = 1, _x_2 = 7, _y_2 = 9.

distance2 = (7 – 1)2 + (9 – 1)2 = 62 + 82 = 100

distance = 10

distance2 = (_x_2 – _x_1)2 + (_y_2 – _y_1)2 + (_z_2 – _z_1)2

= (4 – 2)2 + (6 – 3)2 + (5 – 4)2

= 22 + 32 + 12

= 14

distance = √14

easiest way to do this is by plotting the points and turining it into a right triangle by using delta x and delta y

the delta x is 11-6 = 5

the delta y is 15-3 = 12

those form the two legs of the right triangle; the hypotenuse is the distance

dx2 +dy2= h2

25+144 = h2

169 = h2

h = 13

We can see that the distance between the two points in Quantity A is 4 because they have the same y-coordinate and x-coordinates that are 4 apart (10 – 6).

Quantity B is a little trickier to figure out and requires either the use of the formula below or creating a right triangle out of the two points.

Using the formula √\[(–2 – 1)2 + (4 – 1)2\] is √\[9 + 9\] which equals √18.

Although we don't know the square root of 18 automatically, we know that it will fall between √16 and √25 or 4 and 5. Since Quantity A is 4 and Quantity B has to be between 4 and 5, Quantity B is greater.

The man travels 40 meters north, 100 meters west, and 30 meters east. After he backtracks, he now has a cumulative distance west of 70 meters and he is 40 meters north. His wife has travelled east 60 meters and south 20 meters. Their positions can be modelled by the following points:

We can use the distance fomula to find the distance between the two points.

Half of this distance would be 71.59, approximately 72 meters.

distance2 = (_x_2 – _x_1)2 + (_y_2 – _y_1)2

Looking at the two order pairs given, _x_1 = 1, _y_1 = 1, _x_2 = 7, _y_2 = 9.

distance2 = (7 – 1)2 + (9 – 1)2 = 62 + 82 = 100

distance = 10

distance2 = (_x_2 – _x_1)2 + (_y_2 – _y_1)2 + (_z_2 – _z_1)2

= (4 – 2)2 + (6 – 3)2 + (5 – 4)2

= 22 + 32 + 12

= 14

distance = √14

easiest way to do this is by plotting the points and turining it into a right triangle by using delta x and delta y

the delta x is 11-6 = 5

the delta y is 15-3 = 12

those form the two legs of the right triangle; the hypotenuse is the distance

dx2 +dy2= h2

25+144 = h2

169 = h2

h = 13

We can see that the distance between the two points in Quantity A is 4 because they have the same y-coordinate and x-coordinates that are 4 apart (10 – 6).

Quantity B is a little trickier to figure out and requires either the use of the formula below or creating a right triangle out of the two points.

Using the formula √\[(–2 – 1)2 + (4 – 1)2\] is √\[9 + 9\] which equals √18.

Although we don't know the square root of 18 automatically, we know that it will fall between √16 and √25 or 4 and 5. Since Quantity A is 4 and Quantity B has to be between 4 and 5, Quantity B is greater.

The man travels 40 meters north, 100 meters west, and 30 meters east. After he backtracks, he now has a cumulative distance west of 70 meters and he is 40 meters north. His wife has travelled east 60 meters and south 20 meters. Their positions can be modelled by the following points:

We can use the distance fomula to find the distance between the two points.

Half of this distance would be 71.59, approximately 72 meters.

distance2 = (_x_2 – _x_1)2 + (_y_2 – _y_1)2

Looking at the two order pairs given, _x_1 = 1, _y_1 = 1, _x_2 = 7, _y_2 = 9.

distance2 = (7 – 1)2 + (9 – 1)2 = 62 + 82 = 100

distance = 10

distance2 = (_x_2 – _x_1)2 + (_y_2 – _y_1)2 + (_z_2 – _z_1)2

= (4 – 2)2 + (6 – 3)2 + (5 – 4)2

= 22 + 32 + 12

= 14

distance = √14

The man travels 40 meters north, 100 meters west, and 30 meters east. After he backtracks, he now has a cumulative distance west of 70 meters and he is 40 meters north. His wife has travelled east 60 meters and south 20 meters. Their positions can be modelled by the following points:

We can use the distance fomula to find the distance between the two points.

Half of this distance would be 71.59, approximately 72 meters.

easiest way to do this is by plotting the points and turining it into a right triangle by using delta x and delta y

the delta x is 11-6 = 5

the delta y is 15-3 = 12

those form the two legs of the right triangle; the hypotenuse is the distance

dx2 +dy2= h2

25+144 = h2

169 = h2

h = 13

We can see that the distance between the two points in Quantity A is 4 because they have the same y-coordinate and x-coordinates that are 4 apart (10 – 6).

Quantity B is a little trickier to figure out and requires either the use of the formula below or creating a right triangle out of the two points.

Using the formula √\[(–2 – 1)2 + (4 – 1)2\] is √\[9 + 9\] which equals √18.

Although we don't know the square root of 18 automatically, we know that it will fall between √16 and √25 or 4 and 5. Since Quantity A is 4 and Quantity B has to be between 4 and 5, Quantity B is greater.