Question

What is the distance of point of intersection of straight lines 2x+3y=6 and y=x+7 from origin?​

Answer 1

Step-by-step explanation:

Finding the point of intersection of the two lines by a system of equations.

2x+3y=6----------i)

y=x+7--------------ii)

Substitute eq ii) into i)

2x+3y=6

2x+3(x+7)=6

2x+3x+21=6

5x=6-21

5x=-15

x=-3

Put the value of x in eq ii)

y=x+7

y=-3+7

y=4

Therefore the point of intersection is (-3,4)

Using the distance formula, we will find the distance between the point of intersection and the origin.

d=√[(0-3)²+(0+4)²]

d=√(9+16)

d=√25

d=5 units

Therefore the distance between the point of intersection and the origin is 5 units.

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