Answer:
The perimeter of the polygon formed by the points A(-2,1), B(4,-1), and C(-2,3) is 2√10 + 2√13 + 2 units.
None of the option is true.
Explanation:
To find the perimeter of the polygon formed by the points A(-2,1), B(4,-1), and C(-2,3), we need to calculate the distances between these points and add them together.
First, let's find the distance between points A and B. We can use the distance formula:
dAB = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates of points A(-2,1) and B(4,-1):
dAB = √((4 - (-2))^2 + (-1 - 1)^2)
= √((6)^2 + (-2)^2)
= √(36 + 4)
= √40
= 2√10
Next, let's find the distance between points B and C:
dBC = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates of points B(4,-1) and C(-2,3):
dBC = √((-2 - 4)^2 + (3 - (-1))^2)
= √((-6)^2 + (4)^2)
= √(36 + 16)
= √52
= 2√13
Finally, let's find the distance between points C and A:
dCA = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates of points C(-2,3) and A(-2,1):
dCA = √((-2 - (-2))^2 + (1 - 3)^2)
= √((0)^2 + (-2)^2)
= √(0 + 4)
= √4
= 2
Now, we can add up the distances to find the perimeter:
Perimeter = dAB + dBC + dCA
= 2√10 + 2√13 + 2
Thus,
None of the option is true.