Line through two points

Task number: 2350

Find formuli for the line \(\pi\) in the parametric form \((x,y)=(x_0,y_0)+t(p,q)\), in general form \(ax+by+c=0\), in "division" form \(\frac{x}{g} + \frac{y}{h} = 1\) and in slope-intercept form \(y=kx+l\). The line, goes through points \(A\) and \(B\) at given positions.

Decide, whether the coefficients \(x_0,…, l\) are unique.

  • Variant 1

    \(A=(1{,}2)\) and \(B=(3{,}4)\)

  • Variant 2

    \(A=(-3{,}0)\) and \(B=(2{,}3)\)

  • Variant 3

    \(A=(1,-1)\) and \(B=(2{,}2)\)

  • Variant 4

    \(A=(2,-1)\) and \(B=(2{,}4)\)

  • Variant 5

    \(A=(0{,}1)\) and \(B=(4{,}3)\)

  • Variant 6

    \(A=(2{,}1)\) and \(B=(4{,}2)\)

  • Variant 7

    \(A=(0{,}3)\) and \(B=(-2{,}3)\)

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
Cs translation
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