IF YOU ARE SMART Chris is creating a triangular-shaped garden. He creates a scale drawing with coordinates A, B, and C to repres
ent each corner of the garden. Triangle ABC has vertices located at A(4, 0), B(4, 3) and C(–3, 0).
(a) See in the diagram above the triangle that represents Chris’s garden. Use the formula for the area of a triangle to determine the area of the garden in square units. Show your work.
(b) Chris knows that 1 unit is equivalent to 2 ft on his graph. Chris says that to calculate the area in square feet, he can just double the area that he calculated in square units. Is Chris correct? Explain why or why not.
***Hint You will need to find the area of the triangle in feet***
(c) Chris decides to plant corn in one-third of his garden. Chris wants to plant only four corn plants in each square foot of this section of the garden to ensure each plant has enough room to grow. How many corn plants will he need? Show your work.
***Hint You will need your answer from part b***
2. Sara and three of her friends use an Internet mapping application to map the location of each of their houses. Sara’s house is located at (–2, –5), Nate’s house is located at (–2, 2), Michelle’s house is located at (4, –5), and Joshua’s house is located at (x, y).
(a) On your own paper, plot the three points representing Sara’s, Nate’s, and Michelle’s houses. You don't need to show this graph in your TGA.
(b) The friends discover that the four houses are the vertices of a rectangle. What are the coordinates of Joshua’s house? Explain.
(c) Joshua wants to know how far he would have to ride his bike on a trip from his house to Nate’s then to Sarah’s, then to Michelle’s, and finally back home. Use the appropriate mathematical formula to determine the distance in coordinate units that Joshua would have to ride. Show your work.
(d) Joshua knows that 1 unit on the graph represents 3 mi. He says he can multiply the perimeter of the rectangle in units by 3 to calculate the perimeter in miles. Is Joshua correct? Explain why or why not.
3. The two points on the coordinate plane represent two corners of a large park.
Reflect point A (-2,3) across the x-axis to create point A'. Reflect point B (7,-3) across the x-axis to create point B'. What are the coordinates of point A' and point B'? Explain.
The park is a rectangle formed by all four points. One unit represents 0.5 mi. What is the area of the park in square miles? Show your work. ***Hint You will need to convert to find the answer in miles
4. Drew made a conjecture about the distance between two points on a coordinate plane. He said that if both points have the same x-coordinates, then the distance between the two points is the distance between the two y-coordinates. If both points have the same y-coordinates, then the distance between the two points is the distance between the x-coordinates.
Is Drew correct? Explain.
