In the rectangular coordinate system above, if point R (not

We are given that a triangle is created using the x- and y-axes of the coordinate plane. The vertices of the triangle fall at point P (4,0), the origin (0,0), and point R (0,y). We see that we do not know the y-coordinate of point R. We can sketch it, as follows:



Given that one vertex falls on point (4,0) and the other vertex on point (0,0), we see that our base is equal to 4.

We are also given that the area of the triangle is 12. Using the formula for the area of a triangle and substituting the known values, we obtain:

area = (base x height)/2

12 = (4 x height)/2

24 = 4 x height

6 = height

The information above tells us that the distance between the origin and point R (which is on the y-axis) is 6. Thus, the y-coordinate of point R is 6.

The answer is B.

Hi @Bunnel,

Is it correct to say that the reason why we don't need to use the 'distance between 2 points' formula to get the base in this exercise is because the 2 points lay on the coordinate lines, and not on the coordinate plane? Thanks!

I picked the trap answer A here

Once I drew the right angle Triangle and saw 4 as one of the side - Thanks to repeating 3-4-5 - I wrongly concluded the other two sides as 3 and 5. To top it up 4*3 = 12 which is there in the stem as well, just to give a false sense of security!

Sometimes when we rush to get to an answer, we so easily fall into a neatly laid out trap - Just for us!

The y coordinate will be (Y,0)

X coordinate of the triangle is 4,0

Base =4

1/2*4*h=12

h=6

Answer B

In the rectangular coordinate system above, if point R (not shown) lies on the positive y-axis and the area of triangle ORP is 12, what is the y-coordinate of point R?

\(Area = \frac{1}{2} * Base * Height\)

\(12 = \frac{1}{2} * Base (OP) * Height (OR)\)

\(12 = \frac{1}{2} * 4 * OR\)

\(12 = 2 * OR\)

\(OR = 6\)

As OR lies on Y axis, co-ordinates of point R will be \((0,6)\)
Hence, \(y co-ordinate = 6\)

Hence, Answer is B

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