another great prompt

[DBushkalov]

here's a good one from the GMAT PREP's tasks:


can someone explain to me how we get to s = 1?

I managed to find out that OP = OQ = sqrt3. but does it automatically follow that Q has coordinates (sqrt3; 1) ??

THANK YOU

[Lifetron]

This might help !

https://www.beatthegmat.com/gmat-prep-ge ... t4660.html

[Anju@Gurome]

Refer to the figure below


Now, the two right angle triangles are congruent triangles as their angles have same measures and their hypotenuse are also equal.

Hence, s must be equal to 1 and t must be equal to √3.

The correct answer is B.

[Anju@Gurome]

Algebraic Approach:
Coordinates of point O, the origin is (0, 0).
Angle POQ = 90º, so (the slope of OP)*(slope of OQ) = -1 (the product of the slopes of two perpendicular lines is -1).

We can find the slope of OP, as we know the coordinates of both O and P.
Slope of OP = (1 - 0)/(-√3 - 0) = -1/√3
So, slope of OQ = √3/1 or (√3 - 0)/(1 - 0), which implies the x-coordinate of point Q is 1 or s = 1.

The correct answer is B.