Lesson: Distance between Two Points on a Coordinate Plane

In this lesson, we will learn how to find the distance between two points on the coordinate plane using the Pythagorean theorem.

Video

14:21

Sample Question Videos

  • 03:10
  • 03:44
  • 03:08

Worksheet: 25 Questions • 3 Videos

Q1:

On a map, coordinates are expressed in miles. The coordinates for San Francisco are ( 5 3 , 1 7 ) and those for Sacramento are ( 1 2 3 , 7 8 ) . Find the distance between the cities to the nearest mile.

Q2:

On a map, each coordinate represents a distance in miles from some fixed point. San Jose’s coordinates are (76, − 1 2 ), while those for San Francisco are (53, 17). Find the distance between San Jose and San Francisco to the nearest mile.

Q3:

Points 𝐴 and 𝐵 have coordinates 𝐴 ( 𝑥 , 𝑦 ) and 𝐵 ( 𝑥 , 𝑦 ) respectively. Point 𝐶 lies on 𝐴 𝐵 such that 𝐴 𝐶 and 𝐵 𝐶 are in the ratio of 𝑘 ∶ 𝑚 .

Write the quotient of the length of 𝐴 𝐶 by the length of 𝐴 𝐵 in terms of 𝑘 and 𝑚 .

Find an expression for the difference between the 𝑥 coordinates of 𝐴 and 𝐵 .

Find an expression for the difference between the 𝑦 coordinates of 𝐴 and 𝐵 .

Find an expression for the coordinates of 𝐶 .
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