Coordinate Geometry Test - 1

Since the line cuts x-axis,
y = 0

Given: x = 6 + 2y
x = 6 + 2 × 0 = 6
So, x = 6 + 2y cuts x-axis at (6, 0).

Consider the linear equation of the form y = mx + c. ... (1)
Since (-2, 2) and (0, 0) are solutions of the equation (1);

⇒ 2 = -2m + c
⇒ c - 2m = 2 ... (2)
And

0 = m(0) + c
⇒ c = 0

Using the value of c in equation (2), we get m = -1
Then, the required equation is:
y = -(1)x + 0 ⇒ y + x = 0

We have coordinates (1, 1).
Putting the given coordinates in y = 2x - 1,
1 = 2 × 1 - 1
1 = 2 -1
1 = 1
Hence, the coordinates satisfy the equation y = 2x - 1.

Let the abscissa and ordinate be x and y respectively.

Then, x² + y² = 2 ... (1)
And

xy = 1 ... (2)

Substituting the value of y from (2) in (1) we get,
x² + (1/x)² = 2

x⁴ + 1 = 2x²
(x² - 1)² = 0

x² - 1 = 0
x² = 1
x = 1 or x = -1

Abscissa = 2 + ordinate
An ordered pair consists of two terms - the abscissa (horizontal, usually x) and the ordinate (vertical, usually y).
6 = 2 + ordinate (y)
y = 4

Point A(6,7) has ordinate as 7 and point B(-3, 4) has ordinate as 4.
Thus, (Ordinate of A) - (Ordinate of B) = 7 - 4 = 3