Question

Give the coordinates for point P in the following right trapezoid without using any new variables

Answer 1

The correct answer is b (c,0)

Answer 2

Answer with explanation:

→→Naming of trapezoid =O P QR=O(0,0),P(x,0),Q(a,b) and R (0,c)

Where the Coordinate of vertices of Trapezoid P =(x,0)

→Slope between two points (m,n) and (c,d) is given by

`(n-d)/(m-c)`

→Slope of segment OP,where, O(0,0),and P(x,0),using the above formula

`(0-0)/(x-0)=(0)/(x)`

Similarly, Slope of segment OR,where, O(0,0),and R(0,c),using the above formula

`(c-0)/(0-0)=(c)/(0)`

→Side OP and OR are Perpendicular to each other.

Slope of segment OP × Slope of segment OR= -1

`(0)/(x) * (c)/(0)= -1\\\\ -x=c\\\\ x= -c`

But this point lies on positive side of x axis, so the coordinate of vertices of point P should be (c,0).

There is another way of solving this problem.

Draw perpendicular from Vertex Q(a,b)on X axis.Coordinates of P will become (a,0).

Now, draw perpendicular from vertex R on side PQ.

Opposite sides of rectangle are equal.

OP=MR=a

OR=MP=c

OR ⊥ OP

Product of their slopes ,that is slope of OR and OP= -1

`(0)/(a) * (c)/(0)= -1\\\\ -a=c\\\\ a= -c`

But point ,P lies on positive side of x axis.

So, coordinates of point P = (c,0)

Option B (c,0)