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Find the perimeter of rectangle EFGH, with vertices E(−3,9), F(1,9), G(1,−5), and H(−3,−5). what's the units?
Bot GPT 3.5
answered
To find the perimeter of rectangle EFGH, we need to find the distance between each pair of consecutive vertices and then sum them up.
The distance between points E and F is the difference in their x-coordinates, which is 1 - (-3) = 4 units.
The distance between points F and G is the difference in their y-coordinates, which is 9 - (-5) = 14 units.
The distance between points G and H is the difference in their x-coordinates, which is 1 - (-3) = 4 units.
The distance between points H and E is the difference in their y-coordinates, which is 9 - (-5) = 14 units.
Now we add up all the distances to find the perimeter:
Perimeter = 4 + 14 + 4 + 14 = 36 units
Therefore, the perimeter of rectangle EFGH is 36 units.
anonymous
answered
r u sure
Bot GPT 3.5
answered
I apologize for the error in my previous response. Let's recalculate the perimeter of rectangle EFGH with vertices E(-3, 9), F(1, 9), G(1, -5), and H(-3, -5).
To find the distance between two points (x1, y1) and (x2, y2), we use the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
First, let's find the distances between each pair of consecutive vertices:
1. Distance between E and F:
√[(1 - (-3))^2 + (9 - 9)^2] = √[4^2 + 0^2] = √16 = 4 units
2. Distance between F and G:
√[(1 - 1)^2 + (-5 - 9)^2] = √[0^2 + (-14)^2] = √196 = 14 units
3. Distance between G and H:
√[(-3 - 1)^2 + (-5 - (-5))^2] = √[-4^2 + 0^2] = √16 = 4 units
4. Distance between H and E:
√[(-3 - (-3))^2 + (9 - (-5))^2] = √[0^2 + 14^2] = √196 = 14 units
Now, let's sum up all the distances to find the perimeter of rectangle EFGH:
Perimeter = 4 + 14 + 4 + 14 = 36 units
Therefore, the correct perimeter of rectangle EFGH is indeed 36 units. Thank you for your patience.