What is the difference between a new penny and an old quarter? Only 4 Gen!uses

Find the midpoint between the points (–2, 3) and (4, 2). SOLUTION – () , 2222 ( ) 5252, = 1 ( ) 5252, = The midpoint is, 1 ( ) 5252 x 1 + x 2 2 ( ) y 1 + y 2 2, Remember, the midpoint formula is Finding the Midpoint Between Two Points (Review)

Objective- To solve problems involving the Pythagorean Theorem and Distance Formula. For Right Triangles Only! leg hypotenuse - always opposite the right angle

For Right Triangles Only! leg hypotenuse a b c

a b c Pythagorean Theorem For Right Triangles Only!

6 8 x Solve for x.

6 t 15 Solve for t.

20 miles A car drives 20 miles due east and then 45 miles due south. To the nearest hundredth of a mile, how far is the car from its starting point? 45 miles x

Finding the Distance Between Two Points using the DISTANCE FORMULA Using the Pythagorean theorem (x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 = d 2 THE DISTANCE FORMULA d = (x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 Solving this for d produces the distance formula. You can write the equation a 2a 2 + b 2+ b 2 = c 2= c 2 x 2 – x 1 y 2 – y 1 d x y C (x 2, y 1 ) B (x 2, y 2 ) A (x 1, y 1 ) The steps used in the investigation can be used to develop a general formula for the distance between two points A(x 1, y 1 ) and B(x 2, y 2 ).

Finding the Distance Between Two Points Find the distance between (1, 4) and (–2, 3) using the distance formula. d = (x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 = 10  3.16 Write the distance formula. Substitute. Simplify. Use a calculator. SOLUTION = (x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 –2 – 13 – 4

Applying the Distance Formula A player kicks a soccer ball that is 10 yards from a sideline and 5 yards from a goal line. The ball lands 45 yards from the same goal line and 40 yards from the same sideline. How far was the ball kicked? The ball is kicked from the point (10, 5), and lands at the point (40, 45). Use the distance formula. d = (40 – 10) 2 + (45 – 5) 2 = = 2500 = 50 The ball was kicked 50 yards. SOLUTION