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In the x-y coordinate axis, a perpendicular line AD is drawn from the point A (2,4) on the line x + y = 10 and it is

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by BTGmoderatorDC » Fri Jan 17, 2020 4:16 pm
In the x-y coordinate axis, a perpendicular line AD is drawn from the point A (2,4) on the line x + y = 10 and it is extended till E, such that AD = DE. Find the co-ordinate of E?
A. (-6,-8)
B. (55/13, 44/13)
C. (6, 8)
D. (11, 5)
E. (15,15)



OA C

Source: e-GMAT
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Re: In the x-y coordinate axis, a perpendicular line AD is drawn from the point A (2,4) on the line x + y = 10 and it is

by swerve » Sat Jan 18, 2020 3:06 pm
BTGmoderatorDC wrote: ↑
Fri Jan 17, 2020 4:16 pm
 In the x-y coordinate axis, a perpendicular line AD is drawn from the point A (2,4) on the line x + y = 10 and it is extended till E, such that AD = DE. Find the co-ordinate of E?
A. (-6,-8)
B. (55/13, 44/13)
C. (6, 8)
D. (11, 5)
E. (15,15)



OA C

Source: e-GMAT
The equation of line perpendicular to \(x + y = 10\) is \(y−x−k=0\).

As point A lies on \(y−x−k=0\), point A must satisfy its equation=
\(4-2-k=0\) or \(k=2\).

Hence, the equation of the line perpendicular to \(x + y = 10\) is \(y−x=2\).

We can notice that \(y\) coordinate of any point on this line is 2 units greater than \(x\) coordinate of that point.

Only option __C__ satisfies our condition.
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