1. **Problem 3: Determine if JK \cong MN** Given: - J(-1, 10), K(-5, 2) - M(9, -7), N(1, -3) We need to find the lengths of JK and MN using the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ Calculate JK: $$JK = \sqrt{(-5 - (-1))^2 + (2 - 10)^2} = \sqrt{(-4)^2 + (-8)^2} = \sqrt{16 + 64} = \sqrt{80} = 4\sqrt{5}$$ Calculate MN: $$MN = \sqrt{(1 - 9)^2 + (-3 - (-7))^2} = \sqrt{(-8)^2 + (4)^2} = \sqrt{64 + 16} = \sqrt{80} = 4\sqrt{5}$$ Since $JK = MN$, the segments are congruent. 2. **Problem 5: Find CE given midpoint D and expressions for CD and DE** Given: - D is midpoint of CE - $CD = 9x - 7$ - $DE = 3x + 17$ Since D is midpoint, $CD = DE$ Set equal and solve for $x$: $$9x - 7 = 3x + 17$$ Subtract $3x$ from both sides: $$6x - 7 = 17$$ Add 7 to both sides: $$6x = 24$$ Divide both sides by 6: $$x = 4$$ Find $CD$ and $DE$: $$CD = 9(4) - 7 = 36 - 7 = 29$$ $$DE = 3(4) + 17 = 12 + 17 = 29$$ Total length $CE = CD + DE = 29 + 29 = 58$