The given points are X( 1, 3), Y(8, 3) and Z(2, 1). Here, x1 = 1, y1 = 3, x2 = 8, y2 = 3, x3 = 2 and y3 = 1 Now, we will find the slopes of the XY and YZ. Sl ...

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Standard X

Mathematics

Points on a Cartesian Plane

X-1,3, Y8,-3 ...

Question

X( $-$ 1, 3), Y(8, $-$ 3) and Z(2, 1).

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Solution

The given points are X( $-$ 1, 3), Y(8, $-$ 3) and Z(2, 1).
Here, x₁ = $-$ 1, y₁ = 3, x₂ = 8, y₂ = $-$ 3, x₃ = 2 and y₃ = 1
Now, we will find the slopes of the XY and YZ.
$Slope of X Y = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{- 3 - 3}{8 - (- 1)} = - \frac{6}{9} = - \frac{2}{3} Slope of Y Z = \frac{y_{3} - y_{2}}{x_{3} - x_{2}} = \frac{1 - (- 3)}{2 - 8} = - \frac{4}{6} = - \frac{2}{3}$

The slope of XY is the same as that of YZ and point Y is common to both XY and YZ.
∴ Points X, Y and Z are collinear.

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X(-1, 3), Y(8, -3) and Z(2, 1).

X( $-$ 1, 3), Y(8, $-$ 3) and Z(2, 1).