Slope Station. 2. When are two lines in the plane perpendicular to one another?
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1 Slope Station 1. When are two lines in the plane parallel to each other? When their slopes are equal 2. When are two lines in the plane perpendicular to one another? When their slopes are opposite reciprocals 3. Describe how the slope formula that uses two points which is calculated as is algebraically equivalent to saying slope is the rise over run is the vertical distance between the points, and is the horizontal distance between the points. Therefore the ratio of the vertical and horizontal distances is the rise over the run 4. Determine whether quadrilateral ABCD is a parallelogram, trapezoid, or neither. State how you made your determination. A(0,3), B(1,5), C(4,5), D(3,3) Slope AB = Slope CD = 2, Slope AD = Slope BC = 0, by definition it s a parallelogram since it has two opposite parallel sides. 5. Given that PQRS is a parallelogram, determine whether PQRS is a square. (Do not use distance formula for this problem) P(1,4), Q(3,6), R(5,4), S(3,2) since their points fall on vertical and horizontal lines in the xy plane. This means the quadrilateral is a kite or a rhomubs. But since the segments that meet at P have opposite reciprocal slopes, angle P measures 90 degrees. There for it has to be a Square.
2 DISTANCE STATION 1. Explain in your own words how the distance formula is related to the Pythagorean Theorem. * The Pythagorean theorem applies to right triangles. Since all coordinates in the x,y plane form right angles, the length of the segment connecting them is the hypotenuse of a right triangle. The difference of and and and give the lengths of the leg of a right triangle. 2. A catapult is brought in to lay siege to a medieval castle. The catapult has a maximum effective range of 600 yards. The location of the castle is at (350,513), and the catapult is located at the origin. Assuming 1 unit in the plane is 1 yard, determine if the castle within range of the catapult. Calculation: which is. Since the units are yards, it is about 21 yards too far away. 3. Stacy and Ken are siblings that go to two different schools. They are arguing who has the longer commute to school. Stacy goes to Mount Hopkins High School which is located at (-15,21) and Ken goes to Mount Graham High School, which is located at (20,-12). Who actually has the longer commute to school? Assume their house is the origin. Ken Calculation: Stacy Calculation: which is approx units which is approx units 4. A length of cable must be laid underground to connect two major data hubs. The coordinates of each city are (-10, 23) and (16,6). Each unit in the grid is 1 mile in distance. If they currently have 31 miles of cable at their disposal, should they begin the project? Distance: which is approx miles. They should not start since they need an additional 0.06 miles of cable to make it. * If you wrote a 1 sentence answer to this problem, then you re doing it wrong.
3 MIDPOINT STATION 1. A circle has a center of (3,3) and one end point of a diameter at (7,6). Determine the location of the other endpoint. so and so y=0. The other endpoint should be at 2. A symmetric beam is laying on the ground of a construction site, and must be raised to the top of a skyscraper by a crane. The beam s endpoints are (-1,1), (13,5). Where should the crane cable be placed so the beam is balanced? Midpoint 3. A math teacher is making a quiz about trapezoid midsegments. If the trapezoid has coordinates A(2,1), B(6,7), C(12,7), D(14,1). Determine the coordinates needed to draw the midsegment of the trapezoid. Midpoint, Midpoint 4. Researchers have data about the declining population of a town. They have that in the year 1960 the population was 12,000, and in 1970 the population was 7,000. Approximate the population in The midpoint of the segment will give the approximation of the population, you should treat the information as two ordered pairs. Taking the midpoint you ll get the ordered pair so in 1965 you could expect the population to be around 9,500 people.
4 Congruence Station 1. Prove whether the figures in the x,y plane are congruent. : A(2,4), B(4,11), C(6,4) : D(1,2), E(1,-2), F(8,0) Statements Reasons 1. : A(2,4), B(4,11), C(6,4) : D(1,2), E(1,-2), F(8,0) 1. Given 2. AB=CB=DF=EF= 2. Distance Formula ED=AC=4 3., 3. Definition of By SSS 2. Prove whether the two triangles are congruent. A(2,4), B(5,10), C(7,3) : D(10,5), E(11,12), F(15,6) They are not congruent since has lengths of (approx) 3.61, 6.71, and EF = Since no segment in has that length they can t be congruent.
5 Equations of lines in the plane 1. Give the equation of the line in slope intercept form that passes through the point (1,3) with a slope of Give the equation of a line parallel to that passes through the point (1,1) 3. Give the equation of the line that passes through the points (1,3), (6,7) Slope: Point Slope: 4. A segment has endpoints A(0,2),B (4,4). Give the equation of the perpendicular bisector of Midpoint: (2,3) Slope AB = ½ opposite reciprocal slope: -2 Equation:
6 Polygon Properties Station 1. Prove that A(1,1), B(3,3), C(1,5) is an isosceles right triangle. Statements Reasons 1. A(1,1), B(3,3), C(1,5) is a triangle 1. Given 2. AB = BC = 2. Distance Formula 3. Slope AB = 1, Slope BC=-1 3. Slope formula Opposite Reciprocal Slopes are perpendicular is a right angle 5. Definition of 6. is an isosceles right triangle 6. Definition, steps 2,5 2. Prove that PQRS is a square. P(1,2), Q(3,4), R(5,2), S(3,0) Statements Reasons 1. P(1,2), Q(3,4), R(5,2), S(3,0) 1. Given Is a quadrilateral 2. PQ=QR=RS=PS= 2. Distance formula Definition of 4. Slope PQ = 1, Slope PS=-1 4. Slope formula Opposite reciprocal Slopes are 7. PQRS is a rectangle 7. Theorem PQRS is a square 8. Definition, Steps 6,7
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