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Question 25 : A triangle ABC has area 32 sq units and its side BC, of length 8 units, lies on the line x = 4. Then the shortest possible distance between A and the point (0,0) is

4√2 units
2√2 units
4 units
8 units

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Explanatory Answer

Method of solving this CAT Question from Coordinate Geometry

CAT 2018 Question Paper Quants Slot 2 Coordinate Geometry

Given Area (△ABC) = 32 sq units and one of the length BC = 8 units on the line x = 4
Let us draw a graph and plot the given values.
We know that area of the Triangle = \\frac{1}{2}) × base × height considering BC as the base,
area of the Triangle = \\frac{1}{2}) × 8 × height = 32
Height = \\frac{32 × 2}{8}) = \\frac{64}{8}) = 8 units
Since the base lies on x = 4 and has a vertical height is of length = 8 units, A can either lie on the line x = 12 or on x = - 4
However, since we need to find the shortest possible distance between A and the origin, A should lie on the line x = - 4
So, shortest possible distance to A from the point (0,0) = 4 units

The question is "A triangle ABC has area 32 sq units and its side BC, of length 8 units, lies on the line x = 4. Then the shortest possible distance between A and the point (0,0) is"