Question 85

The distance between the points (4,-8) and (k,0) is 10. Find k?

Solution

Distance between two points $$(x_1 , y_1)$$ and $$(x_2 , y_2)$$ = $$\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}$$

Now, distance between points (4,-8) and (k,0) = 10

=> $$\sqrt{(0 + 8)^2 + (k - 4)^2} = 10$$

=> $$64 + (k^2 - 8k + 16) = (10)^2 = 100$$

=> $$k^2 - 8k = 100 - 64 - 16$$

=> $$k^2 - 8k - 20 = 0$$

=> $$k^2 + 2k - 10k - 20 = 0$$

=> $$k(k + 2) - 10(k + 2) = 0$$

=> $$(k + 2) (k - 10) = 0$$

=> $$k = -2 , 10$$

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