sat-dog

-1,1 Choice C is correct. It’s given that the circle has its center at ^ h and that 5,-4 line t is tangent to this circle at the point ^ h. Therefore, the points -1,1 5,-4 ^ h and ^ h are the endpoints of the radius of the circle at the point of tangency. The slope of a line or line segment that contains the points ^a,bh and d - b -1,1 5,-4 ^c,dh can be calculated as - . Substituting ^ h for ^a,bh and ^ h for d - b c a -4-1 -5 ^c,dh in the expression - yields 5- -1, or 6. Thus, the slope of this radius is -5 c a ^ h 6. A line that’s tangent to a circle is perpendicular to the radius of the circle at the point of tangency. It follows that line t is perpendicular to the radius at the 5,-4 point ^ h, so the slope of line t is the negative reciprocal of the slope of this -5 6 6 radius. The negative reciprocal of 6 is 5. Therefore, the slope of line t is 5. Since the slope of line t is the same between any two points on line t, a point lies 5,-4 6 on line t if the slope of the line segment connecting the point and ^ h is 5. 10,2 5,-4 Substituting choice C, ^ h, for ^a,bh and ^ h for ^c,dh in the expression - -4-2 6 10,2 d b - yields 5-10, or 5. Therefore, the point ^ h lies on line t. c a 49 SAT PRACTICE TEST #5 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2 0,6 Choice A is inco6rrect. The slope of the line segment connecting b 5l and -4- 5,-4 5 -26 6 ^ h is 5-0 , or 25, not 5. Choice B is incorrect. The slope of the line 4,7 5,-4 -4-7 - 6 segment connecting ^ h and ^ h is 5-4 , or 11, not 5. Choice D is 11,1 5,-4 -4-1 incorrect. The slope of the line segment connecting ^ h and ^ h is 5-11, 5 6 or 6, not 5.