Distance Formula Review

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Presentation transcript:

Distance Formula Review DO NOW 11.10: Use the coordinates to find the length of side AB Distance Formula Review (-4, 3) (-6,0) (1,3) (3,0) (-1,0) (4,6) (1,6) Agenda Logo Project/Note Check Distance Formula Review Independent Work Time Debrief

GPS Coordinates and Distance How does GPS work? Latitude – North/South Longitude – East/West Unit Conversion – at our location, one “degree” latitude is about 69 mi. and one “degree” longitude is about 53 mi. So a distance that involves both would be the average, ≈ 61 mi.

Logo Transformation Projects Complete Step 1 and 2. Use distance formula to find the measure of the lengths of the sides.

Debrief How is distance formula used in the real world? How are longitude and latitude related to coordinates?

Neighborhood Groups: Area and Perimeter DO NOW 11/11: What is the perimeter of this quadrilateral? What is the area? 8 in Neighborhood Groups: Area and Perimeter 6 in 6 in 4 in 12 in Agenda Logo Project Check In (10 min) “Neighborhood” Groups: Distance and Scale (15 min) Area and Perimeter (25 min) Debrief (10 min)

Choosing A Scale Identify your maximum and minimum values. Determined the spaces on your graph you will cover with those values. Subtract the two values and divide by the number of spaces to determine the value of each space. Remember: The goal of any good graph is CLARITY!

Distance of Segment AB Distance Formula Pythagorean Theorem A (x1, y1) B(x2, y2) (x2 - x1)2 + (y2 – y1)2 = d2 A (x1, y1) B(x2, y2) y2 – y1 = a x2 – x1 = b a2 + b2 = c2

Perimeter of an Irregular Quadrilateral The perimeter of any quadrilateral is the sum of all of the sides. For quadrilateral ABCD, the perimeter formula would be: P = AB + BC + CD + DA *MUST BE IN NOTES!*

Create Your Own Neighborhood!

Neighborhood Groups: Area and Perimeter DO NOW 11/11: What is the perimeter of this quadrilateral? What is the area? Neighborhood Groups: Area and Perimeter 7cm 6cm Agenda “Neighborhood” Groups: Perimeter and Area(15 min) Logo Work Time(25 min) Debrief (10 min) 15 cm

Debrief How is distance formula used in the real world? How are longitude and latitude related to coordinates? How could we find the area covered by our neighborhoods?

Area of an Irregular Quadrilateral Any quadrilateral can be subdivided into two or more triangles. The area formula for a triangle is A = ½ (b)(h) where b is the base and h is the perpendicular height.

Logo Transformation Project: Final Questions! DO NOW 11/13: Prove that the quadrilateal below is a rhombus. Logo Transformation Project: Final Questions! Logo Design Transformations Proof Area and Perimeter

Logo Design Must have 7 points, 3 quadrilaterals Color to help you visualize transformations!

Transformations Start with original coordinates each time! Translation Reflection Rotation

Reflection

Rotation

Proof Must prove properties of ONE of the quadrilaterals. Slope i.e. How can I prove ABCE is a parallelogram? Slope Distance

Area and Perimeter Must find for whole figure (ALL three quadrilaterals) What is the easiest way to find the area and perimeter of the whole figure? Find ACDB and ACGF