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
(1) y^2−2y−3=0
(2) x^2=y^2
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]
