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# CAT 2018 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Coordinate Geometry Questions | Question 25

This question from CAT 2018 Question Paper becomes a no brainer once you get your method and concepts in place. A very straightforward question from Coordinate Geometry where you are required to deduce the shortest possible distance of a point on traingle from the origin. Solving CAT Previous Year Paper can give your online CAT Preparation a much required boost. Do not wait any longer! Dive into solving this question right away!

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

1. 4√2 units
2. 2√2 units
3. 4 units
4. 8 units

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##### Method of solving this CAT Question from 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"

##### Hence, the answer is 4 units

Choice C is the correct answer

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