# XAT 2015 Quant & DI: Coordinate Geometry Q9

This aptitude practice question appeared in the quantitative reasoning and data interpretation section of the XAT 2015. Question 9 of a total of 33 questions that appeared in this section in XAT 2015. This one is an __easy__ question and tests the concept of finding lengths of line segments given coordinates of two points on the line segment.

## Question

Two diagonals of a parallelogram intersect each other at coordinates (17.5, 23.5). Two adjacent points of the parallelogram are (5.5, 7.5) and (13.5, 16). Find the lengths of the diagonals.

- 15 and 30
- 15 and 40
- 17 and 30
- 17 and 40
- Multiple solution are possible

** Correct Answer** Choice D. The lengths of the diagonals are 17 and 40.

## Explanatory Answer

#### Given Data

- Diagonals of the parallelogram intersect at 17.5, 23.5. Let us call this point O (17.5, 23.5).
- Coordinates of two adjacent points of the parallelogram are (5.5, 7.5) and (13.5, 16)

Let us say the points are A(5.5, 7.5) and B(13.5, 16)

#### Key facts

Diagonals of the parallelogram bisect each other.

i.e., they intersect at their mid-points.

From two adjacent vertices of a parallelogram two different diagonals originate.

So, the diagonal from A will be AC and the one from B will be BD.

Because O is the midpoint of AC, the distance AO will be equal to half AC.

Similarly, the distance BO will be equal to half BD.

#### What is the Approach?

Find OA and OB and double them to get the lengths of the diagonals

The distance between points O(17.5, 23.5) and A(5.5, 7.5)

OA = \\sqrt{ (x_2 - x_1)^2 + (y_2 - y_1)^2 }\\)

= \\sqrt{ (17.5 - 5.5)^2 + (23.5 - 7.5)^2 }\\) = 20

If OA = 20, AC = 2 * OA = 2 * 20 = 40

Similarly, the distance between points O(17.5, 23.5) and B(13.5, 16)

OB = \\sqrt{ (17.5 - 13.5)^2 + (23.5 - 16)^2 }\\) = 8.5

If OB = 8.5, BD = 2 * OB = 2 * 8.5 = 17.

The lengths of the diagonals are 17 and 40

The correct answer is Choice D.

## Video Explanation

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## XAT TANCET Practice Questions - Listed Topic wise

- Number Theory
- Permutation Combination
- Probability
- Inequalities
- Geometry
- Coordinate Geometry
- Mensuration
- Trigonometry
- Data Sufficiency
- Percentages
- Profit Loss
- Ratio Proportion
- Mixtures & Alligation
- Speed Distance & Time
- Pipes, Cisterns & Work, Time
- Simple & Compound Interest
- Races
- Averages & Statistics
- Progressions : AP, GP & HP
- Set Theory
- Clocks Calendars
- Linear & Quadratic Equations
- Functions
- English Grammar
- General Awareness