Unit-7 Coordinate Geometry
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Unit-7 Coordinate Geometry
Answer: Midpoint = ((0+4)/2, (6+0)/2) = (2, 3).
Answer: The line through (2, 3) and (5, 6) is y = x + 1; putting y = 7 gives x = 6.
Answer: Both coordinates are negative, which is the third quadrant.
Answer: (3 + x)/2 = 5 gives x = 7; the y-coordinate checks since (5 + 1)/2 = 3.
Answer: Area = 1/2 x 6 x k = 3k = 15, so k = 5.
Answer: x is positive and y is negative, which is the fourth quadrant.
Answer: x = 8 - 6 = 2 and y = 2 - 2 = 0, so x + y = 2.
Answer: Side lengths are sqrt(29), 5 and 2, and 2^2 + 5^2 = 29, so it is right-angled.
Answer: In the first quadrant both coordinates are positive.
Answer: (a + 3)/2 = 4 gives a + 3 = 8, so a = 5.
Answer: The line is y = 2x; (2, 6) does not satisfy it, so it is not on the line.
Answer: In the second quadrant x is negative and y is positive.
Answer: (2 + x)/2 = 5 gives x = 8.
Answer: p^2 + p^2 = (3sqrt(2))^2 gives 2p^2 = 18, so p = 3 or p = -3.
Answer: In the third quadrant both coordinates are negative.
Answer: Midpoint = ((-4+4)/2, (2-2)/2) = (0, 0).
Answer: x^2 + 144 = 169 gives x^2 = 25, so x = 5 or x = -5.
Answer: In the fourth quadrant x is positive and y is negative.
Answer: Section formula with m = 2, n = 1: x = (2(6) + 1(0))/3 = 4, y = (2(9) + 1(0))/3 = 6.
Answer: Side lengths are 6, 8 and 10 (a 6-8-10 triangle), so perimeter = 6 + 8 + 10 = 24.