Digits, Grade 8, Volume 1, Homework Helper

4-5: Additional Problem Solving

Part 1

Example Using Distance to Locate Points

Point B has coordinates (1, 5). The y-coordinate of point A is −3. The distance between point A and point B is 10 units. What are the possible coordinates of point A?

Solution

Point B has coordinates (1, 5).

Point A has y-coordinate of −3, so it is somewhere along the line y = −3.

Points A, B, and C form a right triangle with eh b bar as the hypotenuse.

The distance between points A and B is 10 units. The length of b c bar is 8 units.

Use the Pythagorean Theorem to find the length of the unknown leg.

table with 6 rows and 2 columns , row1 column 1 , eh squared , plus , b squared , column 2 equals , c squared , row2 column 1 , 8 squared , plus , b squared , column 2 equals , 10 squared , row3 column 1 , 64 plus , b squared , column 2 equals 100 , row4 column 1 , b squared , column 2 equals 36 , row5 column 1 , square root of b squared end root , column 2 equals square root of 36 , row6 column 1 , b , column 2 equals 6 , end table

Point A can be 6 units to the left of point C, or 6 units to the right of point C. So the possible coordinates of point A are (−5, −3) and (7, −3).


End ofPage 149

Table of Contents

Digits, Grade 8, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Proportionality Unit C: Expressions, Equations, and Relationships English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties