Q8 of 20 Page 52

Let us calculate and see that for what value of y, the distance of the two points (2, y) and (10, –9) will be 10.

We know that distance between two points (x1, y1) and (x2, y2) is given by .


Using the above distance formula,


Distance between (2, y) and (10, -9)




Given, distance of the two points (2, y) and (10, –9) = 10.


∴


Squaring both sides, we get


y2 – 18y + 145 = 100


y2 – 18y + 45 = 0


On splitting the middle term,


y2 – 3y- 15y + 45 = 0


y(y – 3) - 15(y – 3) = 0


(y – 15) (y – 3) = 0


So, y can take two values, 15 and 3.


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