Finding Straight Line Equation Through Two Points
We need to find the equation of the straight line that passes through the points $(0, 2)$ and $(1, -3)$.
Calculate the Slope
First, calculate the slope ($m$) using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1) = (0, 2)$ and $(x_2, y_2) = (1, -3)$.
$ m = \frac{-3 - 2}{1 - 0} = \frac{-5}{1} = -5 $
Using the Point-Slope Form
Now, use the point-slope form of a linear equation, which is $y - y_1 = m(x - x_1)$. We can use either point; let's use $(0, 2)$.
$ y - 2 = -5(x - 0) $
Simplify the Equation
Simplify the equation obtained:
$ y - 2 = -5x $
Rearrange the terms to match the standard form $Ax + By + C = 0$:
$ 5x + y - 2 = 0 $
This equation represents the straight line passing through the given points.
Verification
Let's check if the points satisfy the equation $5x + y - 2 = 0$.
- For $(0, 2)$: $5(0) + 2 - 2 = 0 + 0 = 0$. (Satisfied)
- For $(1, -3)$: $5(1) + (-3) - 2 = 5 - 3 - 2 = 0$. (Satisfied)
The derived equation is correct.
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Find the co-ordinates of the centroid of a triangle whose vertices are A(1, 4), B(7, 8) and C(10, 12).
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- \(A(1, 2)\), \(B(a, -26)\), \(C(13, -14)\) and \(D(6, 14)\) are the vertices of a parallelogram, taken in order, find the value of \(a\).
