# DISTANCE BETWEEN TWO POINTS WORD PROBLEMS

## About "Distance between two points word problems"

Distance between two points word problems :

The Pythagorean Theorem can be used to find the distance between two points in a real-world situation. We can do this by using a coordinate grid that overlays a diagram of the real-world situation.

## The Pythagorean Theorem In a right triangle, the sum of the squares of the lengths of the  legs is equal to the square of the length of the hypotenuse.

If a and b are legs and c is the hypotenuse, then

a² + b²  =  c²

## Distance between two points word problems - Examples

Example 1 :

Gabriela wants to find the distance between her house on one side of a lake and the beach on the other side. She marks off a third point forming a right triangle, as shown in the figure. The distances in the diagram are measured in meters. Use the Pythagorean Theorem to find the straight-line distance from Gabriela’s house to the beach. Solution :

Step 1 :

Find the length of the horizontal leg.

The length of the horizontal leg is the absolute value of the difference between the x-coordinates of the points (280, 20) and (10, 20).

|280 - 10|  =  270

The length of the horizontal leg is 270 meters.

Step 2 :

Find the length of the vertical leg.

The length of the vertical leg is the absolute value of the difference between the y-coordinates of the points (280, 164) and (280, 20).

|164 - 20|  =  144

The length of the vertical leg is 144 meters.

Step 3 :

Let a = 270, b = 144 and c represent the length of the hypotenuse. Use the Pythagorean Theorem to write the relationship between a, b and c.

a² + b²  =  c²

Step 4 :

Substitute a = 270 and b = 144 and solve for c.

270² + 144²  =  c²

Simplify.

72,900 + 20,736  =  c²

93,636  =  c²

Take the square root of both sides.

93,636  =

306  =  c

Hence, the distance from Jose’ house to the beach is 306 meters.

Example 2 :

Camp Sunshine is also on the lake. Use the Pythagorean Theorem to find the distance between Gabriela’s house and Camp Sunshine to the nearest tenth of a meter. Solution :

Step 1 :

Find the length of the horizontal leg.

The length of the horizontal leg is the absolute value of the difference between the x-coordinates of the points (200, 20) and (10, 20).

|200 - 10|  =  190

The length of the horizontal leg is 190 meters.

Step 2 :

Find the length of the vertical leg.

The length of the vertical leg is the absolute value of the difference between the y-coordinates of the points (200, 120) and (200, 20).

|120 - 20|  =  100

The length of the vertical leg is 100 meters.

Step 3 :

Let a = 190, b = 100 and c represent the length of the hypotenuse. Use the Pythagorean Theorem to write the relationship between a, b and c.

a² + b²  =  c²

Step 4 :

Substitute a = 190 and b = 100 and solve for c.

190² + 100²  =  c²

Simplify.

36,100 + 10,000 =  c²

46,100  =  c²

Take the square root of both sides.

√46,100  =

√46,100  =  c

Find the value of √46,100 using calculator and round to the nearest tenth

214.7    c

Hence, the distance from Gabriela’a house to the Camp Sunshine is about 214.7 meters. After having gone through the stuff given above, we hope that the students would have understood "Distance between two points word problems".

Apart from the stuff given above, if you want to know more about "Distance between two points word problems", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here. WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6