In the coordinate plane, a triangle has points (4,6), (8,6), and (x,y)

Solution

Given:
• In a given triangle in the coordinate plane, the vertices are (4, 6), (8, 6), and (x, y)

To find:
• Whether the mentioned triangle is isosceles or not

Analysing Statement 1
• As per the information provided in Statement 1, x = 6

o As we already know that the points are forming a triangle, y cannot be equal 6. Otherwise the points will not be able to form a triangle

• As y is not equal to 6, for other values of y we can have many triangles, as shown in the diagram below:



• The line x = 6 is the perpendicular bisector of the line joining the points (4, 6) and (8, 6)

Also, any points on the perpendicular bisector, which are in the form (6, y), will always be equidistant from the points (4, 6) and (8, 6)

• Hence, it will definitely form an isosceles triangle

Therefore, statement 1 is sufficient to answer

Analysing Statement 2
• As per the information provided in Statement 2, y = 9
• Given the y-coordinate of the 3rd point is fixed, the x coordinate can vary and depending on the values of x, we can have multiple possibilities as shown in the diagram below:

• Keeping y = 9, if the value of x is 6 then it forms an isosceles triangle
• But, if x = 5 or x = 8, the triangles formed are not isosceles triangle

As multiple possibilities exist, we cannot get a unique answer from this statement

Hence, statement 2 is not sufficient to answer the question

Hence, the correct answer is option A.

Answer: A