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Understanding the Coordinate Plane: Distance and Midpoint Formulas

This instructional guide delves into the fundamentals of the coordinate plane, focusing on the distance and midpoint formulas. We explore how to calculate the distance between two points using the formula (d = sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}) and understand its application through examples. Additionally, we cover how to find the midpoint of a segment with the formula ((x_1 + x_2)/2, (y_1 + y_2)/2). We also define terms like perpendicular and trisect, enhancing our understanding of geometric concepts in the coordinate plane.

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Understanding the Coordinate Plane: Distance and Midpoint Formulas

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  1. Geometry Honors The Coordinate Plane

  2. The Coordinate Plane y-axis QII QI x-axis QIII QIV origin

  3. The Distance Formula d =  (x2 – x1)2 + (y2 – y1)2 This formula is used to determine the distance between two points in the coordinate plane.

  4. Example: Find the length of RT if R(5,2) and T(-4,-1). d =  (x2 – x1)2 + (y2 – y1)2 Remember, there could be an exact length and a decimal approximate length.

  5. Your Turn: Find the length of QW if Q(5,8) and W(-3,-1). d =  (x2 – x1)2 + (y2 – y1)2

  6. The Midpoint of a Segment b a a + b 2

  7. Example: Find the midpoint of the segment below: -4 -14

  8. The Midpoint of a Segment in the Coordinate Plane   x1+ x2 2 y1+ y2 2 , Midpoint =

  9. Example: Find the midpoint of AB if A(5,8) and B(-3,2). x1+ x2 2 y1+ y2 2 , Midpoint =

  10. Example: The midpoint of AB is M(3,4). One endpoint is A(-3,-2). Find the coordinate of the other endpoint B. x1+ x2 2 y1+ y2 2 , Midpoint =

  11. Definitions: Perpendicular – forms a right angle at the intersection. Symbol:  Trisect– cuts into 3 equal pieces. • You could trisect an angle or a segment.

  12. Definitions: Median of a triangle – a segment which has one endpoint at a vertex of the triangle and the other endpoint at the middle of the opposite side.

  13. Think: The midpoint of TS is the origin. Point T is located in Quadrant II. What quadrant contains point S?

  14. Let’s do the Midpoint Worksheet Together!

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