What type of quadrilateral is formed by connecting the points (0, 9), (3, 6), (0, 1), and (–3, 6)?
rhombus
trapezoid
kite
quadrilateral
kite isa the answr
A graph shows that it is a kite.
(0,1),(0,9). A ver. line.
(-3,6),(3,6). A hor. line.
The line of symmetry is the y-axis(x = 0).
After connecting the 4 given points.
you can complete the graph.
Right kite
Hmm, let me put on my geometry clown nose and think about this. Ah, I've got it! The quadrilateral formed by connecting those points is none other than a trapezoid. It's like a quadrilateral with a little personality, leaning to one side like it's about to break out in dance. Keep an eye on those wacky sides!
To determine the type of quadrilateral formed by connecting the given points, we can use the properties of each quadrilateral type.
A rhombus is a quadrilateral with all sides equal in length. To check if the given points form a rhombus, we can calculate the distances between each pair of adjacent points and see if they are all equal.
A trapezoid is a quadrilateral with one pair of parallel sides. To check if the given points form a trapezoid, we need to examine the slopes of the lines connecting each pair of adjacent points. If any two slopes are equal, then the lines are parallel.
A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. To check if the given points form a kite, we can calculate the distances between each pair of adjacent points and examine the ratios between them.
If none of the above conditions are satisfied, then we can conclude that the given points form a general quadrilateral.
Let's go through these steps to determine the type of quadrilateral formed by connecting the points (0, 9), (3, 6), (0, 1), and (–3, 6):
1. Calculate the distances between each pair of adjacent points:
- Distance between (0, 9) and (3, 6) = sqrt((3 - 0)^2 + (6 - 9)^2) = sqrt(9 + 9) = sqrt(18)
- Distance between (3, 6) and (0, 1) = sqrt((0 - 3)^2 + (1 - 6)^2) = sqrt(9 + 25) = sqrt(34)
- Distance between (0, 1) and (-3, 6) = sqrt((-3 - 0)^2 + (6 - 1)^2) = sqrt(9 + 25) = sqrt(34)
- Distance between (-3, 6) and (0, 9) = sqrt((0 - (-3))^2 + (9 - 6)^2) = sqrt(9 + 9) = sqrt(18)
2. Determine if the distances between adjacent points are equal:
- The distances between adjacent points are not all equal, as sqrt(18) is not equal to sqrt(34) or sqrt(34).
3. Examine the slopes of the lines connecting the points:
- The slope between (0, 9) and (3, 6) is (6 - 9)/(3 - 0) = -1.
- The slope between (3, 6) and (0, 1) is (1 - 6)/(0 - 3) = 5/(-3) = -5/3.
- The slope between (0, 1) and (-3, 6) is (6 - 1)/(-3 - 0) = 5/(-3) = -5/3.
- The slope between (-3, 6) and (0, 9) is (9 - 6)/(0 - (-3)) = 3/3 = 1.
4. Determine if any two slopes are equal:
- The slope between (3, 6) and (0, 1) is equal to the slope between (0, 1) and (-3, 6), which means the lines connecting these pairs of points are parallel.
Based on the above calculations, we can conclude that the given points form a trapezoid.