Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P, Q, and R are to be integers that satisfy the inequalities -4 < or= x < or = 5 and 6 < or= y < or = 16. How many different triangles with these properties could be constructed?
sir, in the below steps i did not understand what is x coordinate for vertex R and Q? what is mean by coordinate is fixed by A?? How and why values 9c1 and 10c1 are used??
We have the rectangle with dimensions 10*11 (10 horizontal dots and 11 vertical). RT is parallel to y-axis and RS is parallel to x-axis.
Choose the (x,y) coordinates for vertex R (right angle): 10C1*11C1;
Choose the x coordinate for vertex S (as y coordinate is fixed by A): 9C1, (10-1=9 as 1 horizontal dot is already occupied by A);
Choose the y coordinate for vertex T (as x coordinate is fixed by A): 10C1, (11-1=10 as 1 vertical dot is already occupied by A).
10C1*11C1*9C1*10C1=9900. Answer: C.
though it might be silly doubt.. pls send if their is any concept that i lack understand this problem.
pls reply, thank you.
I'm happy to help.
This question requires a little visualization and some facility with the x-y plane. The question tells us "Right triangle RST can be constructed in the xy-plane such that RS is perpendicular to the y-axis and the right angle is at R
." This tells us
(a) there is a right angle at R, so RS is perpendicular to RT
(b) RS is parallel to the x-axis, perpendicular to the y-axis --- i.e. horizontal
(c) RT must be parallel to the y-axis, perpendicular to the x-axis --- i.e. vertical
Then, we have to recognize --- all points on the same horizontal line have the same height, so they all have the same y-coordinate. Therefore, we absolutely know that R & S, endpoints of the horizontal line, must have the same x-coordinate.
Similarly ---- all points on any vertical line share the same distance from the y-axis, the same length to the right or the left of the y-axis, so all points on the same vertical line must have the same x-coordinate. Thus, R & T, the endpoints of a vertical line, have the same y-coordinate.
Next, inclusive counting. Seehttp://magoosh.com/gmat/2012/inclusive- ... -the-gmat/
From x = -4 to x = +5, there are (+5) - (-4) + 1 = 10 points, and, similarly, 11 possible y-points.
Does this clear up your question? On precisely which part do you have questions?
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