Coordinate Geometry
3 . D To shift left, subtract from the x-coordinate: 5 − 3 = 2; to shift up, add to the y-coordinate: −4
+ 6 = 2. Choice (A) confuses the x- and y-coordinates, and (B), (C), and (E) confuse the
addition and subtraction.
13 . B The coordinates for midpoint are the averages of the endpoints: . For
segment AB, the midpoint is at = 2, = 5. Choices (A) and (D) incorrectly take
half the coordinate of one of the endpoints. Choice (C) adds, rather than averages, the
endpoints. Choice (E) subtracts, rather than adds, the endpoint coordinates.
19 . E The x-intercept is the point at which a line crosses the x-axis, so the y-value of that point will
always be 0. Plug in 0 for the y in the equation, and solve for x: 0 = 5x + 2 → − 2 = 5x →
= x. The x-intercept is thus , which is (E).
24 . K Use the point-slope formula to determine the slope of line OP:
. The slope of a line perpendicular to this one will have a negative reciprocal slope: , so
(K) is correct.
33 . C To determine the graph of the equation, you must isolate the y by subtracting 8x and dividing
by 4. The resulting equation is y = -2x + 3, which is a line with a slope of -2 and a y-
intercept of 3. Because the y-intercept is positive, the line crosses the y-axis from Quadrant II
to Quadrant I and extends into Quadrant IV. The line never passes through Quadrant III,
eliminating (B), (D), and (E). Choice (A) is a partial answer and does not include Quadrant
I. Alternatively, once the equation is in slope-intercept form, just plug it into your graphing
calculator and look at the graph.
39 . C Find the distance between the points using the distance formula:
. Multiply the
coordinate distance by 20 to get the distance in kilometers. Choices (A) and (E) incorrectly
calculate the distance by adding the coordinates and forgetting to square the differences,
