Manipal Entrance Test 2019 Math Paper

(c) Given that, the base of an isosceles triangle PQR are Q(1,3) and R(−2,7). Let the co-ordinates of point P are (x,y).∵ In an isosceles triangle PQ = PR
i.e. √(x−1)2+(y−3)2 =√(x+2)2+(y−7)2
⇒(x−1)2+(y−3)2 =(x+2)2+(y−7)2
⇒x2−2x+1+y2−6y+9 =x2+4x+4+y2−14y+49
⇒−2x−6y+10=4x−14y+49+4
⇒−6x+8y=43
Here, option (

5

6

,6) satisfies the equation.
∴ Co-ordinate of P are (

5

6

,6)