On the xy co-ordinate plane, point C is (5,-2) and point D is (-2,2.5). The point on line segment CD that is twice as far from C as from D is:
Choose the correct choice from the following answers:	A) (1,-1)	B) (1,1)	C) (2,0.25)	D) (3,-0.5)	E) (3,1)
We want the point on the line that is twice as far from C as it is from D. We can examine the x and y coordinates separately since they are independent.   *It should be noted that there are two solutions to this problem, one point between C and D, and another point with D in the middle of C and the point. We can quickly look at the answer choices and see that all the points are between C and D, therefore we can search for that point using the following method:   Taking the x-coordinate first, the distance between C and D is |(x-coordinate of C) - (x-coordinate of D)|= |5 - (-1)= 
<gadget id="calculator">5 - (-1)</gadget>
<output>6</output>
6   The x-coordinate that is twice as far from C as it is from D (and in between C and D) will be 4 units from C and 2 units from D. So the x coordinate of the point we're looking for is  5-4= 
<gadget id="calculator"> 5-4</gadget>
<output>1</output>
1, or  (-1)+2= 
<gadget id="calculator"> (-1)+2</gadget>
<output>1</output>
1.   Now looking at the y-coordinate, we do the same thing. The distance between C and D is |(-2) - 2.5|= 4.5   The y-coordinate that is twice as far from C as it is from D (and in between C and D) will be 3 units from C and 1.5 units from D. So the y coordinate of the point we're looking for is  (-2)+3= 
<gadget id="calculator"> (-2)+3</gadget>
<output>1</output>
1, or  2.5-1.5= 
<gadget id="calculator"> 2.5-1.5</gadget>
<output>1</output>
1.   So now we have our coordinates of the point on the line that is twice as far from C as it is from (3,-0.5): (3,-0.5)   Answer: (3,-0.5)
<result>D</result>
On the xy co-ordinate plane, point C is (5,-2) and point D is (-2,2.5). The point on line segment CD that is twice as far from C as from D is: