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
Good DS question
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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]
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]
Last edited by mevicks on Mon Oct 21, 2013 8:24 pm, edited 1 time in total.
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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
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
Known is a drop Unknown is an Ocean