# GRE Math : How to find the length of a line with distance formula

## Example Questions

### Example Question #1 : How To Find The Length Of A Line With Distance Formula

find the distance between points x and y

X: (6,3)

Y: (11,15)

19

5

13

12

8

13

Explanation:

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

### Example Question #2 : How To Find The Length Of A Line With Distance Formula

Quantity A: The distance between the points with rectangular coordinates (6,0) and (10,0)

Quantity B: The distance between the points with rectangular coordinates (1,1) and (–2,4)

The relationship cannot be determined from the information given.

The two quantities are equal.

Quantity B is greater.

Quantity A is greater.

Quantity B is greater.

Explanation:

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.

### Example Question #3 : Distance Formula

What is the distance between the two points, (1,1) and (7,9)?

7.5

3

5

10

51/2

10

Explanation:

distance2 = (x2 – x1)2 + (y2 – y1)2

Looking at the two order pairs given, x1 = 1, y1 = 1, x2 = 7, y2 = 9.

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

distance = 10

### Example Question #3 : How To Find The Length Of A Line With Distance Formula

What is the distance between  and ?

Explanation:

distance2 = (x2 – x1)2 + (y2 – y1)2 + (z2 – z1)2

= (4 – 2)2 + (6 – 3)2 + (5 – 4)2

= 22 + 32 + 12

= 14

distance = √14

### Example Question #4 : How To Find The Length Of A Line With Distance Formula

A man travels north 40 meters, while at the same time his wife travels south 20 meters from his initial starting place. He then travels west 100 meters, and his wife travels east 60 meters, followed by him backtracking east 30 meters while his wife stays in the same spot.

Find the approximate value for half the distance between them.

56

220

110

144

72