1. Find the distance between points M(2, -3) and N(10, -3). Step 1: Use the distance formula $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$. Step 2: Substitute values: $$d = \sqrt{(10 - 2)^2 + (-3 - (-3))^2} = \sqrt{8^2 + 0^2}$$. Step 3: Simplify: $$d = \sqrt{64} = 8$$. 2. Distance between P(3, -7) and Q(3, 8). Step 1: Apply formula: $$d = \sqrt{(3-3)^2 + (8 - (-7))^2} = \sqrt{0 + 15^2}$$. Step 2: Simplify: $$d = \sqrt{225} = 15$$. 3. Distance between C(-4, 3) and D(7, 6). Step 1: Calculate differences: $$7 - (-4) = 11, 6 - 3 = 3$$. Step 2: Distance: $$d = \sqrt{11^2 + 3^2} = \sqrt{121 + 9} = \sqrt{130} \approx 11.40$$. 4. Distance between A(2, 3) and B(14, 8). Step 1: Calculate differences: $$14 - 2 = 12, 8 - 3 = 5$$. Step 2: Distance: $$d = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13$$. 5. Distance between X(-3, 9) and Y(2, 5). Step 1: Calculate differences: $$2 - (-3) = 5, 5 - 9 = -4$$. Step 2: Distance: $$d = \sqrt{5^2 + (-4)^2} = \sqrt{25 + 16} = \sqrt{41} \approx 6.40$$. 6. Distance between C(-3, 2) and D(9, 7). Step 1: Differences: $$9 - (-3) = 12, 7 - 2 = 5$$. Step 2: Distance: $$d = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13$$. 7. Distance between S(-4, -2) and T(1, 7). Step 1: Differences: $$1 - (-4) = 5, 7 - (-2) = 9$$. Step 2: Distance: $$d = \sqrt{5^2 + 9^2} = \sqrt{25 + 81} = \sqrt{106} \approx 10.30$$. 8. Distance between K(3, -3) and L(-3, 7). Step 1: Differences: $$-3 - 3 = -6, 7 - (-3) = 10$$. Step 2: Distance: $$d = \sqrt{(-6)^2 + 10^2} = \sqrt{36 + 100} = \sqrt{136} \approx 11.66$$. 9. Distance between E(7, 1) and F(-6, 5). Step 1: Differences: $$-6 - 7 = -13, 5 - 1 = 4$$. Step 2: Distance: $$d = \sqrt{(-13)^2 + 4^2} = \sqrt{169 + 16} = \sqrt{185} \approx 13.60$$. 10. Distance between P(4, 7) and S(-6, -1). Step 1: Differences: $$-6 - 4 = -10, -1 - 7 = -8$$. Step 2: Distance: $$d = \sqrt{(-10)^2 + (-8)^2} = \sqrt{100 + 64} = \sqrt{164} \approx 12.81$$. These calculations follow the distance formula for coordinates on the plane and show exact or approximate distances between each pair of points.