Question

The fair committee wants to print a map to distribute to vendors as they arrive to set up their booths at the fair grounds: On a coordinate grid, the main gato is located at grandstand is located at (1,2) and the games are located at (7.6) Use coordinate goometry to determine which the following statements are true. Select all that apply

A. The single med try use three locations is an acute triangle 3/2
B. The stops between the grandeland and the rides is -3/2
C. The slip between the grandstand the main gate in 2/3
D. The shape beforeen the grandstand an the rides is an acute triangle.
E.The wiangle termed by these three locations is a right triangle

Answer 1

To determine the truth of the statements, we need to analyze the coordinates given and apply concepts of coordinate geometry. Some statements can be proven true, while others cannot be proven or disproven due to insufficient information. The slopes between the grandstand and the rides, and the grandstand and the main gate are true, but the other statements cannot be determined without additional measurements or angles.

Step-by-step explanation:

To determine which of the given statements are true, we need to examine the coordinates and apply concepts of coordinate geometry. Let's analyze each statement:

A. The single mid point between the grandstand and the games is an acute triangle.

To determine if an angle is acute or not, we need three points. However, the given statement only mentions a single midpoint, which is not enough information to determine the angles of a triangle. So, this statement cannot be proven or disproven.

B. The slope between the grandstand and the rides is -3/2.

We can calculate the slope using the coordinates of the grandstand (1,2) and the games (7,6). The slope formula is (y2-y1)/(x2-x1). Substituting the values, we get (-3/2), which means the slope between the grandstand and rides is indeed -3/2. So, this statement is true.

C. The slope between the grandstand and the main gate is 2/3.

Using the coordinates of the grandstand (1,2) and the main gate (7,6), we calculate the slope and find it to be 2/3. So, this statement is true.

D. The shape between the grandstand and the rides is an acute triangle.

By looking at the given coordinates, we can form a triangle with the grandstand, rides, and games. To determine if it is acute or not, we need to calculate the angles using the distance formula and apply trigonometry. However, without further measurements or angles provided, we cannot determine if it is an acute triangle. So, this statement cannot be proven or disproven.

E. The angle formed by these three locations is a right triangle.

Based on the given coordinates, we can calculate the distances between the grandstand, rides, and games using the distance formula. Then, using the Pythagorean Theorem, we can check if the sum of the squares of two shorter sides is equal to the square of the longest side. If it is, then it is a right triangle. Without the exact distances, we cannot verify if it is a right triangle. So, this statement cannot be proven or disproven.