Good DS question

[rakeshd347]

If vertices of a triangle have coordinates (−1,1), (4,1), and (x,y), what is the area of the triangle?
(1) y^2−2y−3=0

(2) x^2=y^2

[mevicks]

Q: We need to find the Area of the triangle

Given: Two coordinates, third is unknown
(also note: we can find the length of one side by distance formula)



St1:
y² - 2y - 3 = 0
(y - 3)(y + 1) = 0
y = 3 OR y = -1
Now, no matter what the x value of (3, x) or (-1, x) is we can still find the distance from that point to the base (base length can be found out by distance formula)

The above figure shows some sample triangles with the same base and height.

Thus we can find the value of (1/2)bh
SUFFICIENT

St2:
x² = y²
x = -y or x = y
There could be n number of values of x and the corresponding value of y would change accordingly.
We cannot find the value of the height, INSUFFICIENT

[spoiler]Answer: A[/spoiler]

[Uva@90]

Hi Rakesh,
Area of triangle = 1/2(b*h)
We need base and height to find the area of triangle

If you plot (-1,1) and (4,1) in graph you will get base of 5.

so the point (x,y) will be either above or below the line of two points (-1,1) and (4,1)

so it is enough if we find the value of y in the point (x,y) to find the area of triangle.

Statement1: y^2 -2y -3 = 0
By solving we get y = 3 or y = -1
Ir-respective of value Y =3 or y = -1, it will be either 2 points above or below of the base line.

hence height = 2

So, area = 1/2 (5)(2) = 5

Hence Statement1 is sufficient.

Statement2: x^2 = y^2
which mean |x| = |y|
so it could be of any value.
Hence insufficient.

So answer is A