Three vertices of a rectangle are given. Find the coordinates of the fourth vertex.
1 answer:
Start with two vertex points from one side of the rectangle:
(4, 0) and (2, -3).
Subtract the X coordinates: 4 - 2 = 2
Subtract the Y coordinates: 0 - -3 = 3
Now, start with the third vertex point that is given:
(-2,4).
The differences for the X & Y coordinates between the third vertex point and the fourth vertex point will be the same as the differences between the 1st and 2nd points, so start with the 3rd point X coordinate and subtract 2 from it to get the X coordinate for the fourth point:
-2 - 2 = -4.
Then, take the 3rd point Y coordinate and subtract 4 to get the Y coordinate for the fourth point:
4 - 3 = 1
So, your fourth vertex point is (-4, 1).
See the attached picture.
This works because each of the two sets of sides of a rectangle are parallel to each other.
(4, 0) and (2, -3).
Subtract the X coordinates: 4 - 2 = 2
Subtract the Y coordinates: 0 - -3 = 3
Now, start with the third vertex point that is given:
(-2,4).
The differences for the X & Y coordinates between the third vertex point and the fourth vertex point will be the same as the differences between the 1st and 2nd points, so start with the 3rd point X coordinate and subtract 2 from it to get the X coordinate for the fourth point:
-2 - 2 = -4.
Then, take the 3rd point Y coordinate and subtract 4 to get the Y coordinate for the fourth point:
4 - 3 = 1
So, your fourth vertex point is (-4, 1).
See the attached picture.
This works because each of the two sets of sides of a rectangle are parallel to each other.
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Answer:
Step-by-step explanation:
Let the sides of a triangle be 6x,8x and 10x.
Perimeter of the triangle, P = 96 cm
We need to find the area of the triangle.
P = sum of all sides
6x+8x+10x = 96
24x = 96
x = 4
Sides are :
6x = 6(4) = 24 cm
8x = 8(4) = 32 cm
10x = 10(4) = 40 cm
Area,
So, the area of the triangle be .