In the xy coordinate plane, does the point (3,4) lie on line t?
(1) The line 5y-45=-x is perpendicular to the line t.
(2) The line with the equation y=(3/4)x−11 intersects the line t when y=-11.
The OA is C.
Please show a step by step approach here and explain why it is not sufficient each statement alone. Thanks.
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In the xy coordinate plane, . . .
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Say the equation of line t is given by y = mx + c; where m = magnitude of slopes of the line and c = y-interceptVincen wrote:In the xy coordinate plane, does the point (3,4) lie on line t?
(1) The line 5y-45=-x is perpendicular to the line t.
(2) The line with the equation y=(3/4)x−11 intersects the line t when y=-11.
The OA is C.
Please show a step by step approach here and explain why it is not sufficient each statement alone. Thanks.
Statement 1: The line 5y-45=-x is perpendicular to the line t.
If a line is perpendicular to each other, the product of their magnitude of slopes is equal to - 1.
Let's find out the magnitude of the line 5y - 45 = -x
We can write 5y - 45 = -x as y = (-1/5)x + 45/5 => magnitude = -1/5
=> m.(-1/5) = - 1
m = 5. Thus, the magnitude of the line t is 5, however, we do not have any idea about c. We cannot determine whether the point (3,4) lies on line t. Insufficient.
Statement 2: The line with the equation y=(3/4)x − 11 intersects the line t when y = -11.
By plugging-in y = -11 in the equation y = (3/4)x − 11, we get -11 = 3x/4 - 11 => x = 0.
Thus, the equation of line t is y = c. however, we do not have any idea about c. We cannot determine whether the point (3,4) lies on line t. Insufficient.
Statement 1 & 2:
Even after combining the two statements, we cannot get the value of c. Insufficient.
The correct answer: C
Hope this helps!
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