The coordinates of the points R,S AND T are (2,a),(9,0)and(-1,4) respectively.

Find the value of a if RS=RT

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Apply distance formula

d=`sqrt((x-x_1)^2+(y-y_1)^2)`

Thus

RS=`sqrt((9-2)^2+(0-a)^2)` (i)

RT=`sqrt((-1-2)^2+(4-a)^2)` (ii)

By given condition

`sqrt(49+a^2)=sqrt(9+14+a^2-8a)`

squaring both side ,we have

`49+a^2=23+a^2-8a`

`26=-8a`

`26/(-8)=a`

`a=-26/8`

Ans.

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