Unit-7 Coordinate Geometry
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Unit-7 Coordinate Geometry
Answer: Let the point be (0, y); equating distances gives (y-1)^2 = (y+3)^2, so y = -1, i.e. (0, -1).
Answer: On the x-axis the y-coordinate is 0; (3, 0) has a positive abscissa.
Answer: d = sqrt((2-(-1))^2 + (3-(-1))^2) = sqrt(9 + 16) = sqrt(25) = 5.
Answer: Let the point be (x, 0); equating distances gives (x-1)^2 = (x-7)^2, so x = 4, i.e. (4, 0).
Answer: Every point on the x-axis has the form (x, 0).
Answer: d = sqrt((0-4)^2 + (3-0)^2) = sqrt(16 + 9) = sqrt(25) = 5.
Answer: Using the x-coordinate: 4m/(m+n) = 2 gives m = n, so the ratio is 1 : 1 (the midpoint).
Answer: Every point on the y-axis has the form (0, y).
Answer: d = sqrt((0-(-4))^2 + (3-0)^2) = sqrt(16 + 9) = sqrt(25) = 5.
Answer: Using the x-coordinate: 6m/(m+n) = 2 gives 2m = n, so m : n = 1 : 2.
Answer: Its y-coordinate is 0, so it lies on the x-axis.
Answer: Midpoint = ((2+8)/2, (5+1)/2) = (5, 3).
Answer: Slope of (1, 1) to (3, 5) is 2 and of (3, 5) to (4, 7) is 2, so the points are collinear.
Answer: Its x-coordinate is 0 and y is negative, so it lies on the negative y-axis.
Answer: Midpoint = ((-3+7)/2, (2-6)/2) = (2, -2).
Answer: (6-2)^2 + (1-y)^2 = 25 gives (1-y)^2 = 9, so y = 4 or y = -2.
Answer: Both coordinates are positive, which is the first quadrant.
Answer: Midpoint = ((-2+6)/2, (-4+0)/2) = (2, -2).
Answer: a^2 + (2a)^2 = (5sqrt(5))^2 gives 5a^2 = 125, so a = 5 or a = -5.
Answer: x is negative and y is positive, which is the second quadrant.