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You have prizes to reveall Go to your gam On the coordinate plane, the segment from G(-6,-2) to H(-3,2) forms one side of a rectangle. The rectangle has a perimeter of 30 units. Find the area of the rectangle.

User KaronatoR
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Answer:

To find the area of the rectangle, we need to first determine the dimensions of the rectangle. We know that one side of the rectangle is the segment from G(-6, -2) to H(-3, 2), and the perimeter of the rectangle is 30 units.

The perimeter of a rectangle is given by the formula: P = 2(l + w), where l is the length and w is the width of the rectangle.

In this case, the length of the rectangle is the distance between points G and H, and the width is the distance between points G and a point on the same horizontal line as H.

First, let's find the length (L):

Distance Formula:

The distance between two points (x1, y1) and (x2, y2) is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

For points G(-6, -2) and H(-3, 2):

d = √((-3 - (-6))^2 + (2 - (-2))^2)

d = √(3^2 + 4^2)

d = √(9 + 16)

d = √25

d = 5 units

Now, we have the length (L) as 5 units.

Next, let's find the width (W):

The width is the distance between G(-6, -2) and a point on the same horizontal line as H(-3, 2). Since the x-coordinate of H is -3, the width is the absolute difference between the x-coordinates of G and H:

W = |x-coordinate of H - x-coordinate of G|

W = |-3 - (-6)|

W = |-3 + 6|

W = |3|

W = 3 units

Now, we have the width (W) as 3 units.

We can now calculate the area (A) of the rectangle:

A = Length (L) x Width (W)

A = 5 units x 3 units

A = 15 square units

So, the area of the rectangle is 15 square units.

Explanation:

User Tejeshree
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