DSQ: Calculating whether point is on a line with an equation - GMAT Quantitative Reasoning
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Determine whether the points are collinear.
Statement 1: The three points are 
Statement 2: Slope of line 
and the slope of line 
Determine whether the points are collinear.
Statement 1: The three points are
Statement 2: Slope of line
Points are collinear if they lie on the same line. Here A, B, and C are collinear if the line AB is the same as the line AC. In other words, the slopes of line AB and line AC must be the same. Statement 2 gives us the two slopes, so we know that Statement 2 is sufficient. Statement 1 also gives us all of the information we need, however, because we can easily find the slopes from the vertices. Therefore both statements alone are sufficient.
Points are collinear if they lie on the same line. Here A, B, and C are collinear if the line AB is the same as the line AC. In other words, the slopes of line AB and line AC must be the same. Statement 2 gives us the two slopes, so we know that Statement 2 is sufficient. Statement 1 also gives us all of the information we need, however, because we can easily find the slopes from the vertices. Therefore both statements alone are sufficient.
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Given:
Find 
.
I) 
.
II) The 
coordinate of the minmum of 
is 
.
Given:
Find
I)
II) The
By using I) we know that the given point is on the line of the equation.
So I) is sufficient.
II) gives us the y coordinate of the minimum. In a quadratic equation, this is what "c" represents.
Therefore, c=-80 and II) is also sufficient.
By using I) we know that the given point is on the line of the equation.
So I) is sufficient.
II) gives us the y coordinate of the minimum. In a quadratic equation, this is what "c" represents.
Therefore, c=-80 and II) is also sufficient.
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Find whether the point 
is on the line 
.
I) 
is modeled by the following: 
.
II) 
is equal to five more than 3 times the y-intercept of 
.
Find whether the point
I)
II)
To find out if a point is on line with an equation, one can simply plug in the point; however, this is complicated here by the fact that we are missing the x-coordinate.
Statement I gives us our function.
Statement II gives us a clue to find the value of 
. 
is five more than 3 times the y-intercept of 
. So, we can find the following:
To see if the point 
is on the line 
, plug it into the function:
This is not a true statement, so the point is not on the line.
To find out if a point is on line with an equation, one can simply plug in the point; however, this is complicated here by the fact that we are missing the x-coordinate.
Statement I gives us our function.
Statement II gives us a clue to find the value of
To see if the point
This is not a true statement, so the point is not on the line.
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Line m is perpendicular to the line l which is defined by the equation 
. What is the value of 
?
(1) Line m passes through the point 
.
(2) Line l passes through the point 
.
Line m is perpendicular to the line l which is defined by the equation
(1) Line m passes through the point
(2) Line l passes through the point
Statement 1 allows you to define the equation of line m, but does not provide enough information to solve for 
. There are still 3 variables 
and only two different equations to solve.
if 
, statement 2 supplies enough information to solve for b by substitution if 
is on the line.
Statement 1 allows you to define the equation of line m, but does not provide enough information to solve for
if
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Consider linear functions 
and 
.
I) 
at the point 
.
II) 
Is the point 
on the line 
?
Consider linear functions
I)
II)
Is the point
Consider linear functions h(t) and g(t).
I) 
at the point 
II) 
Is the point 
on the line h(t)?
We can use II) and I) to find the slope of h(t)
Recall that perpendicular lines have opposite reciprocal slope. Thus, the slope of h(t) must be 
Next, we know that h(t) must pass through (6,4), so lets us that to find the y-intercept:
Next, check if (10,4) is on h(t) by plugging it in.
So, the point is not on the line, and we needed both statements to know.
Consider linear functions h(t) and g(t).
I)
II)
Is the point
We can use II) and I) to find the slope of h(t)
Recall that perpendicular lines have opposite reciprocal slope. Thus, the slope of h(t) must be
Next, we know that h(t) must pass through (6,4), so lets us that to find the y-intercept:
Next, check if (10,4) is on h(t) by plugging it in.
So, the point is not on the line, and we needed both statements to know.
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