plot the given points in a coordinate plane.then determine whether the line segments named are congruent.
A(2,2),B(2,-1),C(0,-2),D(3,-2);
_ and _
AB CD
Line AB is vertical and has length 3.
ine CD is horizontal and has length 3.
So, AB and CD are congruent.
E(-3,2),F(1,2),G(2,3),H(2,-2); EF and GH
To plot the given points on a coordinate plane, follow these steps:
1. Set up a coordinate plane with x-axis (horizontal) and y-axis (vertical).
2. Plot the point A at (2,2). It means that we move 2 units right from the origin (0,0) along the x-axis and 2 units up along the y-axis.
3. Plot the point B at (2,-1). It means we move 2 units right from the origin along the x-axis and 1 unit down along the y-axis.
4. Plot the point C at (0,-2). It means we stay at the x-axis (since x = 0) and move 2 units down along the y-axis.
5. Plot the point D at (3,-2). It means we move 3 units right from the origin along the x-axis and stay at the y-axis (since y = -2).
Now that we have plotted the points (2,2), (2,-1), (0,-2), and (3,-2) on the coordinate plane, let's determine whether the line segments AB and CD are congruent or not.
To determine whether two line segments are congruent, we need to calculate their lengths using the distance formula or by visually comparing them. Let's use the distance formula:
The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
1. For line segment AB:
x₁ = 2, y₁ = 2
x₂ = 2, y₂ = -1
d_AB = √[(2 - 2)² + (-1 - 2)²]
= √[0 + 9]
= √9
= 3
2. For line segment CD:
x₁ = 0, y₁ = -2
x₂ = 3, y₂ = -2
d_CD = √[(3 - 0)² + (-2 - (-2))²]
= √[9 + 0]
= √9
= 3
Since the lengths of line segments AB and CD are both 3 units, they are congruent.
To plot the given points on a coordinate plane, follow these steps:
1. Draw the x-axis (horizontal line) and the y-axis (vertical line), intersecting at the origin (0,0).
2. Label the x-axis and y-axis appropriately with positive and negative numbers.
3. Locate point A(2,2) by moving 2 units to the right along the x-axis and then 2 units up along the y-axis. Plot a point at that location.
4. Locate point B(2,-1) by moving 2 units to the right along the x-axis and then 1 unit down along the y-axis. Plot a point at that location.
5. Locate point C(0,-2) by moving directly down 2 units along the y-axis starting from the origin. Plot a point at that location.
6. Locate point D(3,-2) by moving 3 units to the right along the x-axis and then staying at the same height along the y-axis. Plot a point at that location.
After plotting the points, you can determine if the line segments AB and CD are congruent by comparing their lengths. To do this, measure the distances between the corresponding points using a ruler or by counting the grid units.
For segment AB:
- Measure the distance between points A(2,2) and B(2,-1). It should be 3 units.
For segment CD:
- Measure the distance between points C(0,-2) and D(3,-2). It should also be 3 units.
Since both line segments AB and CD have the same length of 3 units, they are congruent.