Geometry: Distance/ Midpoints. Do Now: Check in Problem (do this by yourself and it will be taken and graded as a hw grade) Directions: Find the value.

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Presentation transcript:

Geometry: Distance/ Midpoints

Do Now: Check in Problem (do this by yourself and it will be taken and graded as a hw grade) Directions: Find the value of x and YZ if Y is between X and Z.

Finding The Midpoint

Generalize Finding Midpoint on a number line:

Examples: AB has endpoints at -4 and 9. What is the coordinate of its midpoint?

But…. Midpoint in Plane

Generalize

Example EF has endpoints E(7, 5) and F(2, -4). What are the coordinates of its midpoint M?

Examples Try the other two on your own!

Examples (continued) Finding an endpoint : The midpoint of CD is M(-2, 1). One endpoint is C(-5, 7). What are the coordinates of the other endpoint D?

Examples (continued) The midpoint of AB has coordinates (4, -7). Endpoint A has coordinates (-3, -5). What are the coordinates of B?

Definitions: Distance: The distance between two points is the length of the segment with those points as it’s endpoints. Ex:

Generalize So…. What’s the general formula for distance on a number line?

But…. Distance in a coordinate plane

Hmmmm… Use the Pythagorean Theorem!!!!!

Distance in a Coordinate Plane:

Distance Formula:

Example What is the distance between U(-7, 5) and V(4, -3)? Round to the nearest tenth.

Example SR has endpoints S(-2, 5) and R(3, -1). What is SR to the nearest tenth?

Exit Ticket: What is the distance of a line with endpoints (-2, 5) and (8, -3)? Leave it as a square root (don’t write it as a decimal) What is the midpoint of the same line?