Cordinate goemetry

[siddharth11.sharma]

In the X-Y coordinate system, what is the slope of the line that goes through the origin and is equidistant from the two points P (1,11) and Q (7,7)?

A) 2
B) 2.25
C) 2.50
D) 2.75
E) 3

[hiteshwd]

Good question, it had me pondering over it for an hour. Ok, here is a GMAt friendly and time saving solution:

Given the line is equidistant from the two points (1,11) and (7,7), the mid point of these two points must lie on the line
i.e. (4,9) must lie on the line.

Now, we know two points i.e. (0,0) and (4,9) that the line passes through, we can calculate the slope as (9-0)/(4-0) = 2.25

Answer B

[siddharth11.sharma]

oh......thanx very much for the guidence!

it was really resourceful.

[siddharth11.sharma]

One more ques:

If p and q are nonzero numbers, and p is not equal to q, in which quadrant of the coordinate system does point (p,p-q) lie?
1) (p,q) lies in quadrant IV.
2) (q,-p) lies in quadrant III.

[hiteshwd]

Sure

Given: p,q not equal to 0 and p not equal to q

1) (p,q) lies in quad IV, which means p is positive and q is negative
=> p-q = +ve
=> p, p-q should lie in quad I as both are positive

SUFFICIENT

2) (q,-p) lies in quad III
=> p = +ve and q = -ve
which takes us onto the same process as in 1)

SUFFICIENT

Sol: D

[siddharth11.sharma]

thanx again:

In the xy-coordinate system, rectangle ABCD is inscribed within a circle having the equation x^2+y^2=25. Line segment AC is a diagonal of the rectangle and lies on the x-axis. Vertex B lies in quadrant II and vertex D lies in quadrant IV. If side BC lies on line y=3x+15. what is the area of rectangle ABCD?

[hiteshwd]

Given:
a line equation & circle's equation, radius of circle = 5 and position of 4 points of rectangle

Solution: Soving the two equations we can get two points B & C where the line and circle intersect i.e. (-5,0) and (-4,3)

We can now draw the figure and know that to calculate the area of rectangle, we need to calculate the area or one triangle and multiply by 2

Area of triangle ABC = 1/2 * B * H = 1/2 * 10 * 3 = 15
Hence, area of rectangle is 30

[jlucero]

3 for 3. Well explained hiteshwd.