MILEAGE MADNESS
Find the distance between the points A(2,3) and B(5,7).
5 UNITS
If A(0,0) and B(6,8) are the endpoints of a line segment, find its midpoint.
(3,4)
On a map, two cities are located at coordinates (3, 5) and (7, 9). If a new road is to be built connecting the two cities, and you want to locate a rest stop that is 2/3 of the way from the first city to the second, what are the coordinates of the rest stop?
(17/3 , 23/3)
A triangular park has vertices at points E(1, 4), F(5, 7), and G(3, 1). What is the area of the park?
9 sq. units
In triangle ABC, the vertices are A(2,4),B(6,8), and C(4,2). What are the coordinates of the centroid GGG of the triangle?
(4, 14/3)
A drone flies from point P(-2,-4) to point Q(-6,1) on a coordinate grid. What is the straight-line distance it travels?
6.40 OR 6.4 UNITS
The midpoint of a line segment is (4, 3). One endpoint is (1, 5). What are the coordinates of the other endpoint?
(7,1)
A circle has a diameter with endpoints at (2, 5) and (8, 11). Find the equation of the line that divides the diameter in a 3:2 ratio.
(5.6, 8.6) or (28/5 , 43/5)
A rectangular field has vertices at points A(2, 3), B(5, 3), C(5, 7), and D(2, 7). What is the area of the field?
12 sq. units
If the coordinates of the vertices of triangle DEF are D(1,2), E(3,4), and F(5,6), calculate the centroid of the triangle.
(3,4)
A point P(5,−2) is reflected over the x-axis to point Q(5,2). Find the distance between points P and Q.
4 UNITS
On a map, two cities are located at coordinates (3, 5) and (7, 9). If you want to find a location that is equidistant from both cities, what are the coordinates of that location?
(5,7)
On a map, two cities are located at coordinates (3, 5) and (7, 9). If a new road is to be built connecting the two cities, and you want to locate a rest stop that is 2 units beyond the second city, what are the coordinates of the rest stop?
(15,17)
A rectangle has vertices at points A(0, 0), B(0, 12), C(8, 12), and D(8, 0). What is the length of the diagonal AC?
14.4 or 14.42 units
A triangle has vertices at P(−2,1), Q(4,5), and R(6,−3). Where is the centroid located?
(8/3 , 1)
If you walk 3 blocks north and then 10 blocks east, how far are you from your starting point if the starting point is in (-2,-15)?
A boat is traveling from point A to point B. If point A is located at (3, 5) and point B is located at (8, 12), find the coordinates of the halfway point.
(11/8 , 17/2) or (5.5, 8.5)
A line segment connecting points (2, 3) and (5, 7). Extend the line segment by 3 units beyond point B. What are the coordinates of the new endpoint?
(14,19)
A quadrilateral-shaped park has vertices at points H(1, 4), I(5, 7), J(8, 2), and K(3, 1). What is the total length of the fence needed to enclose the park?
19.5 or 19.54 units
A triangle ABC has vertices at A(0,0), B(4,0), and C(0,6). What is the centroid of triangle ABC?
(4/3, 2)
A ship sails 20 miles due north and then 15 miles due west. How far is the ship from its starting point plotted in the origin?
25 MILES
A circle has a diameter with endpoints at (2, 5) and (8, 11). Find the coordinate of its center.
(5,8)
Find the length of the radius of a circle with center at (4,-2) and a point on the circle at (-8,6). Determine the coordinates of the other endpoints.
(16,-10)
The owner of an irregular pentagonal farm with vertices (-1, 3), (-3, 1), (0, -2), (3, 1), and (3, 4) is unsure about its correct area. The geodetic engineer calculated the area to be 21 square meters, but the land title states it as 24 square meters. Which area is accurate?
A. The area computed by geodetic engineer
B. The area stated in the land title
C. No one computed the right area
A. The area computed by geodetic engineer
Calculate the centroid of triangle DEF with vertices at D(3,5), E(7,1), and F(5,9).
(5,5)