Find the length of the perpendicular draw from the point `(4,-7)` upon the straight line passing through the origin and the point of intersection of the lines `2x – 3y+ 14 = 0` and `5x + 5y = 7`

Explanation

Given the two lines, `2x−3y+14=0⟶(1)`

`5x+5y−7=0⟶(2)`

Solving these lines we have,

`x/( 21−70)​=y/(70+14)​=1/(10+15)`

=>`x/(−49)​=y/(84)​=1/(25)`
​=>`x=−49/25​,y=84/25`
​
So, `(−49/25​,84/25​)` is the point of intersection of the lines (1) and (2).

`therefore` The equation of the line passing through the origin and the point `(−49/25​,84/25​)` is,
` y−0=(84/25-0)/(-49/25-0)​(x−0)`

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