Three vertices of a rectangle are (-4,2) , (-4,5) and (3,5) plot these points and find the co-ordinates of the fourth vertex . Also find the area and perimeter of the rectangle .
Answers
The coordinates of the fourth vertex of the rectangle for given three vertices are (3, 5)
Finding the coordinates of the fourth vertex of rectangle using graph paper:
As the first step, plot the given three vertices of rectangle on graph sheet as A, B, C. We have to find the fourth vertex D.
From graph, AB = 7 cm and BC = 3 cm.
We know that, opposite sides of a rectangle are parallel and equal.
Therefore, AB = DC = 7 cm and BC = AD = 3 cm.
To find D, plot a point which is 3 cm above A and 7 cm to the left of C.
The point so obtained is (3, 5) which is the fourth vertex D of rectangle.
Answer:
Your 4 points of the rectangle are
A(−4,5),B(−4,2),C(3,2),D(x,y)
From inspection, we can see that A and B have the same x value, and it is most likely that this rectangle is not slanted as B and C have the same y value. Let's continue from here:
From point B to point A, the y value increased by 3, so we can say that from point C to point D the y value should also increase by 3 units. We can therefore deduce that the y value of D=(2+3)=5. Which also is the y value of point A. Now for the x values...
From point B to point D the x value increases by 7, so we can say that the x value should also increase by 7 from point A to point D... Therefore the x value of D is (−4+7)=3 (Which is the same x value as point C
Sometimes it is hard to understand how the graph looks by just reading the points, so let's make it graphical:
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