Let's solve the problem step by step.
First, we need to determine the ratio of the area of rectangle ABEF to the area of rectangle ACDF.
### Step 1: Determine the midpoint coordinates
For a line segment connecting points A and E, the midpoint is:
\[
\text{Midpoint of AE} = \left( \frac{0 + 11}{2}, \frac{6 + 10}{2} \right) = (5.5, 8)
\]
For a line segment connecting points A and F, the midpoint is:
\[
\text{Midpoint of AF} = \left( \frac{0 + 5}{2}, \frac{6 + 2}{2} \right) = (2.5, 4)
\]
### Step 2: Calculate the length and width of rectangles
The coordinates for points are:
- \(D(14,14)\)
- \(E(11,10)\)
- \(F(5,2)\)
- \(A(0,6)\)
**For Rectangle ABEF**:
- Length (horizontal distance between A and E): \( |11 - 0| = 11 \)
- Width (vertical distance between A and F): \( |6 - 2| = 4 \)
Area of Rectangle ABEF:
\[
\text{Area} = 11 \times 4 = 44 \text{ square units}
\]
**For Rectangle ACDF**:
- Length (horizontal distance between A and D): \( |14 - 0| = 14 \)
- Width (vertical distance between A and F): \( |6 - 2| = 4 \)
Area of Rectangle ACDF:
\[
\text{Area} = 14 \times 4 = 56 \text{ square units}
\]
**Ratio of the areas** (Area of Rectangle ABEF : Area of Rectangle ACDF):
\[
\frac{44}{56} = \frac{22}{28} = \frac{11}{14}
\]
None of the options directly match the fraction \(\frac{11}{14}\), which suggests rechecking point or dimension derivations may show ratio closer fitting options.
### Step 3: Calculate individual areas
### Step 4: Calculate the perimeter of rectangle BCDE
Coordinates for points B, C, D, and E:
- \(B(11, 10)\)
- \(C(0,6)\)
- \(D(14,14)\)
- \(E(11,10)\)
The distance between points:
- \(B\) to \(C\): \(\sqrt{ (11-0)^2)+(10-6)^2 } = \sqrt{11*11+4*4} = \sqrt{137}\approx 11.704 \)
- \(C\) to \( E\)
\[
C(11, 10),\quad D(5,4), coordinate B (14-11)^2+(14-10)^2\}\sqrt^2\approx5*0
\]
\[
\text{The perimeter is } 2*6+7.14)*2+24=48.
Different points between both rectangles.
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Select the correct answer from each drop-down menu.
Line segment ABC is parallel to line segment DEF
D(14,14) E(11,10) F(5,2)
In the figure, the ratio of the area of rectangle ABEF to the area of rectangle ACDF is A. 2:1 B. 2:3 C. 3:4 D. 3:5
If the coordinates of point A are (0,6), the area of rectangle ABEF is A. 32.02 B. 48.03 C. 64.03 D. 96.05 square units, and the area of rectangle ACDF is A. 48.03 B. 64.03 C. 96.05 D. 128.07
The perimeter of rectangle BCDE is A. 20.61 B. 28.81 C. 25.61 D. 32.81 units.
1 answer