GMAT Quant Chapter 18: Coordinate Geometry

Question 1

How do we determine the slope of a line?

Answer 1

Y2 - Y1
/
X2 - X1

(Rise / Run)

Question 2

What is the slope of a vertical line and why?

What is the slope of a horizontal line and why?

Answer 2

Undefined because the denominator is 0

0 because the numerator is 0 & 0 divided by anything is0.

Question 3

What is the equation of a line? (slope, intercept)

Answer 3

y =mx + b

y is the y coordinate for a point on the line
x is the corresponding x coordinate for the point on the line
m is the slope of the line
b is the y-intercept of the line

Question 4

How can we graph a line using the slope intercept line equation?

Answer 4

Calculate the x, y-intercepts by setting both x and y to 0, then find another point on the line and connect them

Question 5

How many points on a line do we need in order to define the slope and intercept?

Answer 5

any 2 points on the line

Question 6

What is the product of two reciprocals?

Answer 6

1

Question 7

On Reflections:
reflect the point (x,y) over the following objects:

1. X axis
2. Y axis
3. Origin
4. x=y
5. -x = y
6. y=b
7. x=a

Answer 7

The point (x,y) becomes…

1. (x,-y)
2. (-x,y)
3. (-x,-y)
4. (y,x)
5. (-y,-x)
6. (x, 2b - y)
7. (2a -x, y)

Question 8

How do we determine the distance between 2 points?

e.g (x1, y1) and (x2,y2)

Answer 8

Pythagoras Theorem

change in x^2 + change in y^2 = distance ^2

always x2 - x1 & y2 - y1

Question 9

How do we find the midpoint of a line?

Answer 9

x1 + x2 / 2 & y1 + y2 / 2

Question 10

What is the coordinate geometry equation for a circle?

What is the equation of a circle when its centre is the origin?

Answer 10

(x-a)^2 + (y-b)^2 = r^2

Center (a,b)
radius r

(x)^2 + (y)^2 = r^2

Question 11

For the following inequalities on a graph, where will the highlighted region be in relation to the line…

1. y > mx + b
2. y < mx +b

Answer 11

1. region is above the line
2. region is below the line