If a pair of opposite vertices of parallelogram are (1,3) and (-2,4) and the sides are parallel to `5x-y=0` and `7x+y=0`, then the equation of a side through (1,3) is

Options

A. `5x-y=2`
B. `7x+y=10`
C. `5x-y+14=0`
D. `7x+y+10=0`

Answer

To find the equation of a side of the parallelogram that passes through the point (1,3) and is parallel to the given lines, we will follow these steps:

### Step 1: Identify the slopes of the given lines
The equations of the lines are:
1. \( 5x - y = 0 \)
2. \( 7x + y = 0 \)

To find the slopes, we can rewrite these equations in slope-intercept form \( y = mx + b \).

1. For \( 5x - y = 0 \):
\[ y = 5x \quad \text{(slope = 5)} \]

2. For \( 7x + y = 0 \):
\[ y = -7x \quad \text{(slope = -7)} \]