1.9 Distance & Midpoint Formulas Circles Objectives –Find the distance between two points. –Find the midpoint of a line segment. –Write the standard form.

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Presentation transcript:

1.9 Distance & Midpoint Formulas Circles Objectives –Find the distance between two points. –Find the midpoint of a line segment. –Write the standard form of a circle’s equation. –Give center & radius of a circle whose equation is in standard form. Pg. 239 # 4-48 every other even, 62, 68 (For #44 and 48, make your own graph grid by hand on your paper.) Note: Do NOT convert fractional or radical values to decimals! Maintain the numerical form from the question to the answer!

Suppose you're given the two points (–2, 1) and (1, 5), and they want you to find out how far apart they are. The points look like this: You can draw in the lines that form a right- angled triangle, using these points as two of the corners: The Distance Formula is a variant of the Pythagorean Theorem that you used back in geometry. Here's how we get from the one to the other:

The Distance Formula is a variant of the Pythagorean Theorem that you used back in geometry. Here's how we get from the one to the other: Then use the Pythagorean Theorem to find the length of the third side (which is the hypotenuse of the right triangle): c 2 = a 2 + b 2...so: Copyright © Elizabeth Stapel All Rights Reserved This format always holds true. Given two points, you can always plot them, draw the right triangle, and then find the length of the hypotenuse. The length of the hypotenuse is the distance between the two points. Since this format always works, it can be turned into a formula: Distance Formula: Given the two points (x 1, y 1 ) and (x 2, y 2 ), the distance between these points is given by the formula: It's easy to find the lengths of the horizontal and vertical sides of the right triangle: just subtract the x-values and the y-values:

1. Find the distance between (-4, 9) and (1, -3)

Midpoint is the point in the middle. Therefore the x-value is the average of the 2 given x’s and the y-value is the average of the 2 given y’s. Midpoint of 2. Find the midpoint of the line segment with endpoints (1, 2) and (7, -3)

Standard Form of a Circle with radius = r and center at (h, k) Write the standard form of the equation for a circle with the given center and radius. 3.Center = (0, 0) 4. Center = (5, -6) Radius = 4 Radius = 10

Standard Form of a Circle with radius = r and center at (h, k) A circle centered at (-2,5) with a radius=7 has what equation? A circle whose equation is has what as its center and radius? center = (2,-6) and radius=2

5.Find the center and radius of the circle whose equation is (x + 3) 2 + (y – 1) 2 = 4 6.Graph the circle from question 5: 7.What is the circle’s domain? 8.What is the circle’s range?