1
Question
ABC is an isosceles triangle. If the coordinates of the base are B (1,3) and C (- 2, 7), the coordinates of vertex
A can be
ABC is an isosceles triangle. If the coordinates of the base are B (1,3) and C (- 2, 7), the coordinates of vertex
A can be
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Solution
The correct option is C
The vertex A(x, y) is equidistant from B and C because ABC is an isosceles triangle. Therefore,
(x−1)2+(y−3)2=(x+2)2+(y−7)2
⇒ 6x - 8y + 43 = 0
Thus, any point lying on this line can be the vertex A except the mid-point (−12,5) of BC.
note: A lies on perpendicular bisector of BC
The vertex A(x, y) is equidistant from B and C because ABC is an isosceles triangle. Therefore,
(x−1)2+(y−3)2=(x+2)2+(y−7)2
⇒ 6x - 8y + 43 = 0
Thus, any point lying on this line can be the vertex A except the mid-point (−12,5) of BC.
note: A lies on perpendicular bisector of BC