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<="" div="">="font-size: 14px;">Algebra Coordinate Geometry
1. Since the x-coordinate of R is –1, R lies on the line with equation x = –1. The figure below shows points A (–3,–3) and B (1,–3), the line x = –1, and R with x-coordinate –1 and arbitrary y-coordinate y.
Since the point (–1,–3) is the midpoint of the horizontal segment 
and the vertical line x = –1 contains (–1,–3), the line x = –1 is the perpendicular bisector of 
. Every point on the perpendicular of 
is equidistant from A and B. Since R is on the line x =–1, R is equidistant from A and B.
Alternatively, by the distance formula, the distance between (–3,–3) and R is
Also by the distance formula, the distance between (1,–3) and R is
Since the distance between (–3,–3) and R is the same as the distance between (1,–3) and R, it follows that R is equidistant from (–3,–3) and (1,–3); SUFFICIENT.
2. Given that R is on the line y = –3, the y-coordinate of R is –3. Since the x-coordinate of R is not specified, R could be at multiple locations on the line y = –3, as shown in the chart and figure below; NOT sufficient.
x-coordinate | distance from (–3,–3) | distance from (1,–3) | equidistant? |
–1 | 2 | 2 | yes |
3 | 6 | 2 | no |
The correct answer is A;
statement 1 alone is sufficient.
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