# Coordinate Geometry Practice : Equation of lines

This aptitude question tests your understanding of basic properties of lines, given equation of the lines. The best way to solve such questions is to go from answer choices. This one is a __medium level difficulty__ question. Concepts include properties of concurrent lines, point of intersection of lines, and types of quadrilaterals.

## Question

**Concepts Covered**1. Parallelogram

2. Squares

3. Equation of lines

4. Point of intersection of lines 4 concepts

The equations of four lines are given: x + 2y - 3 = 0, 3x + 4y - 7 = 0, 2x + 3y - 4 = 0 and 4x + 5y - 6 = 0. What can be said about the four lines?

- Concurrent
- Form sides of a parallelogram
- Form sides of a square
- None of these

** Correct Answer** Choice (4). None of these.

## Explanatory Answer

#### Approach : Go from answer choices

##### Choice 1: The four lines are concurrent

If the 4 lines are concurrent, all 4 of them will meet at one point.**Step 1**: Let us find the point of intersection of x + 2y - 3 = 0 and 2x + 3y - 4 = 0

Solving the two equations, we get the point of intersection as (-1, 2).

**Step 2**: Let us check whether the point (-1, 2) lies on the line 4x + 5y - 6 = 0

Substituting x and y values as -1 and 2 respectively, we get 4(-1) + 5(2) - 6 = 0.

Substituting the values of x and y satisfied the equation and hence the point of intersection lies on this line as well.

**Step 3**: Let us check whether the point (-1, 2) lies on the line 3x + 4y - 7 = 0 to conclude whether the lines are concurrent.

Substituting x and y values as -1 and 2 respectively, we get 3(-1) + 4(2) - 7 = -2.

Had the point been a part of the line, it would have satisfied the equation and we would have got 0 as the answer.

Because all 4 lines do not pass through the same point, the four lines are NOT concurrent

##### Choices 2 & 3: Form sides of a parallelogram and form sides of a square

As three of the lines pass through one point they cannot form sides of a quadrilateral.

∴ the four lines CANNOT form sides of either a parallelogram or a square

The correct answer is Choice (4).

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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