# GRE® Coordinate Geometry

#### Concepts Tested from Coordinate Geometry in the GRE

Length of a line segment joining two points, coordinates of a point P that lies on a line segment and divides the line segment in a given ratio, computing the slope of a line if the coordinates of two points through which the line passes is known, testing for collinearity of three or more points, finding the equation of a line and that of parallel and perpendicular lines, computing coordinates of centroid, orthocenter and circumcenter of a triangle, finding equations of median, perpendicular bisector, altitude and angle bisector of a triangle coordinates of whose vertices are known, finding radius of a circumscribing circle, equations of circles, and distance between a point and a line.

1. A straight line 4x + 3y = 24 forms a triangle with the coordinate axes. What is the distance between the orthocentre of the triangle and the centre of the circle that circumscribes the triangle?

1. 10 units
2. 5 units
3. 13 units
4. 12 units
5. 9 units
Approach to solve this Coordinate Geometry Question

Step 1: Compute the coordinates of the Triangle.
Step 2: Determine the coordinates of the orthocentre.
Step 3: Determine the coordinates of the circumcentre.
Step 4: Compute the length of the line segment.

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
Approach to solve this GRE Quantitative Comparison Question

Step 1: Quantity A: Compute the length of the line segment joining the x and y intercepts of 4x + 3y = 12.
Step 2: Quantity B: Compute the coordinates of the mid point D.
Step 3: Quantity B: Compute the length of the median AD.
Step 4: The Comparison: Compare the length of the line segment joining x and y intercepts of 4x + 3y = 12 and the median AD of the triangle given in Quantity B.

#### GRE Online Course - QuantTry it free!

Register in 2 easy steps and
Start learning in 5 minutes!

##### 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

##### How to reach Wizako?

Phone: (91) 44 4500 8484
Mobile: (91) 93800 48484
WhatsApp: WhatsApp Now
Email: learn@wizako.com