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Given the vertices of parallelogram FGHJ in the standard (x, y) coordinate plane below, what is the area of triangle GHJ, in square units?
- a)11
- b)15
- c)22
- d)44
- e)88
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Given the vertices of parallelogram FGHJ in the standard (x, y) coordi...
The area of a triangle is 1/2(bh), where b is the base, and h is the height. You can determine the base by measuring the distance along the x-axis, and you can determine the height by measuring the distance along the y-axis:
The distance between −1 and 3 on the x-axis is 4 units; likewise, the distance between −2 and 2 on the x-axis is 4 units. The length of the base is 4.
The distance between −8 and 3 on the y-axis is 11. The height is 11.
Now plug these values into the formula for the area of a triangle:
The distance between −1 and 3 on the x-axis is 4 units; likewise, the distance between −2 and 2 on the x-axis is 4 units. The length of the base is 4.
The distance between −8 and 3 on the y-axis is 11. The height is 11.
Now plug these values into the formula for the area of a triangle:
Community Answer
Given the vertices of parallelogram FGHJ in the standard (x, y) coordi...
To find the area of triangle GHJ, we need to know the coordinates of the vertices G, H, and J. However, the question does not provide this information. In order to determine the area, we can use the fact that parallelograms have opposite sides that are equal in length and parallel.
- Parallelogram Properties:
- Opposite sides of a parallelogram are parallel.
- Opposite sides of a parallelogram are equal in length.
- Opposite angles of a parallelogram are equal in measure.
- Adjacent angles of a parallelogram are supplementary (add up to 180 degrees).
Since FGHJ is a parallelogram, we can use these properties to find the area of triangle GHJ.
- Approach:
1. Determine the length of one side of the parallelogram.
2. Use the length and the height of the parallelogram to find the area of the parallelogram.
3. Divide the area of the parallelogram by 2 to find the area of triangle GHJ.
- Step 1: Determine the length of one side of the parallelogram.
- Since opposite sides of a parallelogram are equal in length, we can choose any pair of opposite sides to find the length.
- Let's consider side FG and side HJ.
- The length of side FG can be found using the distance formula: √((x2 - x1)^2 + (y2 - y1)^2).
- Let's assume the coordinates of F are (x1, y1) and the coordinates of G are (x2, y2).
- Substitute the coordinates into the distance formula to find the length of side FG.
- Step 2: Use the length and the height of the parallelogram to find the area of the parallelogram.
- The height of the parallelogram can be found by measuring the perpendicular distance between side FG and side HJ.
- Since opposite sides of a parallelogram are parallel, the height is the perpendicular distance between any pair of parallel sides.
- Let's consider the height between side FG and side HJ.
- The area of the parallelogram can be found by multiplying the length of side FG by the height.
- Step 3: Divide the area of the parallelogram by 2 to find the area of triangle GHJ.
- Since triangle GHJ is half of parallelogram FGHJ, its area is half of the area of the parallelogram.
By following these steps, we can find the area of triangle GHJ. However, since the coordinates of the vertices F, G, H, and J are not provided, we cannot calculate the length of side FG or the height of the parallelogram. Therefore, we cannot determine the area of triangle GHJ. Hence, the correct answer cannot be determined from the information given.
- Parallelogram Properties:
- Opposite sides of a parallelogram are parallel.
- Opposite sides of a parallelogram are equal in length.
- Opposite angles of a parallelogram are equal in measure.
- Adjacent angles of a parallelogram are supplementary (add up to 180 degrees).
Since FGHJ is a parallelogram, we can use these properties to find the area of triangle GHJ.
- Approach:
1. Determine the length of one side of the parallelogram.
2. Use the length and the height of the parallelogram to find the area of the parallelogram.
3. Divide the area of the parallelogram by 2 to find the area of triangle GHJ.
- Step 1: Determine the length of one side of the parallelogram.
- Since opposite sides of a parallelogram are equal in length, we can choose any pair of opposite sides to find the length.
- Let's consider side FG and side HJ.
- The length of side FG can be found using the distance formula: √((x2 - x1)^2 + (y2 - y1)^2).
- Let's assume the coordinates of F are (x1, y1) and the coordinates of G are (x2, y2).
- Substitute the coordinates into the distance formula to find the length of side FG.
- Step 2: Use the length and the height of the parallelogram to find the area of the parallelogram.
- The height of the parallelogram can be found by measuring the perpendicular distance between side FG and side HJ.
- Since opposite sides of a parallelogram are parallel, the height is the perpendicular distance between any pair of parallel sides.
- Let's consider the height between side FG and side HJ.
- The area of the parallelogram can be found by multiplying the length of side FG by the height.
- Step 3: Divide the area of the parallelogram by 2 to find the area of triangle GHJ.
- Since triangle GHJ is half of parallelogram FGHJ, its area is half of the area of the parallelogram.
By following these steps, we can find the area of triangle GHJ. However, since the coordinates of the vertices F, G, H, and J are not provided, we cannot calculate the length of side FG or the height of the parallelogram. Therefore, we cannot determine the area of triangle GHJ. Hence, the correct answer cannot be determined from the information given.
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Given the vertices of parallelogram FGHJ in the standard (x, y) coordinate plane below, what is the area of triangle GHJ, in square units?a)11b)15c)22d)44e)88Correct answer is option 'C'. Can you explain this answer?
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