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Points that two lines pass through are given in the table. Match each point of intersection to the correct pair of lines.

Points that two lines pass through are given in the table. Match each point of intersection-example-1

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Answer:

Explanation:

case 1)

Line 1

Let A (2,5) B (-3,-5)

Line 2

Let C (3,0) D (0,-3)

Find the equation of the line 1

Line 1

Let A (2,5) B (-3,-5)

slope m=(y2-y1) /(x2-x1)------> m=(-5-5) /(-3-2)-----> m=2

with m=2 and the point A (2,5) find the equation of the line 1

y-y1=m*(x-x1)------->y-5=2*(x-2)------>y=2x-4+5------> y=2x+1

Find the equation of the line 2

Line 2

Let C (3,0) D (0,-3)

slope m=(y2-y1) /(x2-x1)------> m=(-3-0) /(0-3)-----> m=1

with m=1 and the point C (3,0) find the equation of the line 2

y-y1=m*(x-x1)------->y-0=1*(x-3)------>y=x-3

using a graph tool

see the attached figure N 1

the solution is the point (-4,-7)

case 2)

Line 1

Let A (1,1) B (2,3)

Line 2

Let C (0,3) D (2,5)

Find the equation of the line 1

Line 1

Let A (1,1) B (2,3)

slope m=(y2-y1) /(x2-x1)------> m=(3-1) /(2-1)-----> m=2

with m=2 and the point A (1,1) find the equation of the line 1

y-y1=m*(x-x1)------->y-1=2*(x-1)------>y=2x--2+1------> y=2x-1

Find the equation of the line 2

Line 2

Let C (0,3) D (2,5)

slope m=(y2-y1) /(x2-x1)------> m=(5-3) /(2-0)-----> m=1

with m=1 and the point C (0,3) find the equation of the line 2

y-y1=m*(x-x1)------->y-3=1*(x-0)------>y=x+3

using a graph tool

see the attached figure N 2

the solution is the point (4,7)

case 3)

Line 1

Let A (1,0) B (0,-1)

Line 2

Let C (0,3) D (-2,-1)

Find the equation of the line 1

Line 1

Let A (1,0) B (0,-1)

slope m=(y2-y1) /(x2-x1)------> m=(-1-0) /(0-1)-----> m=1

with m=1 and the point A (1,0) find the equation of the line 1

y-y1=m*(x-x1)------->y-0=1*(x-1)------>y=x-1

Find the equation of the line 2

Line 2

Let C (0,3) D (-2,-1)

slope m=(y2-y1) /(x2-x1)------> m=(-1-3) /(-2-0)-----> m=2

with m=2 and the point C (0,3) find the equation of the line 2

y-y1=m*(x-x1)------->y-3=2*(x-0)------>y=2x+3

using a graph tool

see the attached figure N 3

the solution is the point (-4,-5)

case 4)

Line 1

Let A (2,0) B (0,-2)

Line 2

Let C (4,5) D (3,3)

Find the equation of the line 1

Line 1

Let A (2,0) B (0,-2)

slope m=(y2-y1) /(x2-x1)------> m=(-2-0) /(0-2)-----> m=1

with m=1 and the point A (2,0) find the equation of the line 1

y-y1=m*(x-x1)------->y-0=1*(x-2)------>y=x-2

Find the equation of the line 2

Line 2

Let C (4,5) D (3,3)

slope m=(y2-y1) /(x2-x1)------> m=(3-5) /(3-4)-----> m=2

with m=1 and the point C (4,5) find the equation of the line 2

y-y1=m*(x-x1)------->y-5=2*(x-4)------>y=2x-8+5-----> y=2x-3

using a graph tool

see the attached figure N 4

the solution is the point (1,-1)

User Sergey Fedorov
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