ashishsj wrote: ↑Mon Feb 02, 2009 6:01 pm
10. What are the coordinates of point B in the xy-plane above ?
(A) (6, 12)
(B) (6, 28)
(C) (8, 20)
(D) (12, 20)
(E) (14, 28)
Can anybody help?
Solution:
Since AB = BC, triangle ABC is an isosceles triangle, and BD, the altitude, divides AC, the base, into two equal parts. In other words, AD = DC, and D is the midpoint of AC. Therefore, the x-coordinate of point D is (-8 + 20)/2 = 6, which is also the x-coordinate of point B (notice that we can eliminate choices C, D, and E). Lastly, since AC = BD, and the length of AC is 20 - (-8) = 28, the y-coordinate of point B is the y-coordinate of D plus 28. In other words, the y-coordinate of point B is 0 + 28 = 28. Therefore, the coordinates of point B are (6, 28).
Answer: B 
