Question

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Three vertices of a rectangle pqrs are p(-2,-2),Q(4,-2),R(4,2).Locate these points on a Cartesian plane and hence find the fourth vertex S.Also find the area of the rectangle

Answer 1

Your 4 points of the rectangle are

A(−4,5),B(−4,2),C(3,2),D(x,y)A(−4,5),B(−4,2),C(3,2),D(x,y)

From inspection, we can see that AA and BBhave the same xx value, and it is most likely that this rectangle is not slanted as BB and CC have the same y value. Let's continue from here:

From point BB to point AA, the yy value increased by 3, so we can say that from point CC to point DD the yy value should also increase by 3 units. We can therefore deduce that the yy value of D=(2+3)=5D=(2+3)=5. Which also is the yyvalue of point AA. Now for the xx values...

From point BB to point DD the x value increases by 7, so we can say that the xxvalue should also increase by 7 from point AA to point DD... Therefore the xxvalue of D is (−4+7)=3(−4+7)=3 (Which is the same xx value as point CC

Sometimes it is hard to understand how the graph looks by just reading the points, so let's make it graphical:

I hope this helped ;

Answer 2

hope you understand
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