# GRE® Quant Practice | Coordinate Geometry Q2

#### GRE Quantitative Comparison - Length of 2 Line Segments

This GRE quant practice question is a quantitative comparison question in coordinate geometry. Concept Tested: Finding length of two line segments based on different data available abouts these segments and comparing which of the two lines is longer.

Question 2 : Quantitative Comparison

Quantity A Quantity B
Length of the segment of the line 4x + 3y = 12 intercepted between the coordinate axes. Length of the median to side BC of triangle whose coordinates are A(4, 4), B(10, 4) and C(4, 12)

1. Quantity A is greater
2. Quantity B is greater
3. The two quantities are equal
4. Cannot be determined

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#### Compute the x intercept of the line 4x + 3y = 12:

The y coordinate of the point at which the line intercepts the x axis is 0.
Therefore, to compute the x-intercept of a line, substitute the value of y as 0 in the equation of the line.
Equation of the line, 4x + 3y = 12
4x + 3(0) = 12 → 4x = 12 or x = 3.
Therefore, the x-intercept of the line is 3.

#### Compute the y intercept of the line 4x + 3y = 12

Equation of the line, 4x + 3y = 12
4(0) + 3y = 12 → 3y = 12 or y = 4.
Therefore, the y-intercept of the line is 4.

#### Compute the length of the line segment joining the x and y intercepts of 4x + 3y = 12:

Coordinates of one of the x and y intercept of the line are (3, 0) and (0, 4) respectively.
Length of a line segment, coordinates of whose end points are (x1, y1) and (x2, y2) is $$sqrt{$x_2 - x_1$^2 + (y_2 - y_2)^2})

#### Compute the coordinates of the mid point D of side BC:

The coordinates of the midpoint of a line segment BC, coordinates of whose end points are B(x1, y1) and C(x2, y2) = ($$frac{x_1 + x_2}{2}$ , $\frac{y_1 + y_2}{2}$) The coordinates of the end points of BC are B$10, 4) and C(4, 12).
So, the coordinates of the midpoint D = ($$frac{10 + 4}{2}$,$\frac{4 + 12}{2}$) =$7, 8)

#### Compute the length of the median AD:

Length of a line segment, coordinates of whose end points are (x1, y1) and (x2, y2) is $$sqrt{$x_2 - x_1$^2 + (y_2 - y_2)^2})
The coordinates of the end points of median AD are A(4, 4) and D(7, 8).
Therefore, length of median AD = $$sqrt{$7 - 4$^2 + (8 - 4)^2}) = $$sqrt{$3$^2 + (4)^2}) = $$sqrt{25}$ = 5 units #### The Comparison Quantity A: Length of the segment of the line 4x + 3y = 12 is 5 units Quantity B: Length of the median to the side BC is 5 units Both quantities are equal. #### Choice C is the correct answer #### GRE Online Course - QuantTry it free! Register in 2 easy steps and Start learning in 5 minutes! #### Already have an Account? #### GRE Live Online Classes Next Batch August 26, 2022 ##### Where is Wizako located? Wizako - GMAT, GRE, SAT Prep An Ascent Education Initiative 14B/1 Dr Thirumurthy Nagar 1st Street Nungambakkam Chennai 600 034. India Work @ Wizako ##### How to reach Wizako? Mobile:$91) 93800 48484
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