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Coordinate Geometry — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsCoordinate Geometry3 Marks
Question
From the adjacent figure:
(i) Write the coordinates of the points $A, B$, and

(ii) Write the slope of the line $AB.$
(iii) Line through $C,$ drawn parallel to $AB$, intersects $Y$-axis at $D.$ Calculate the co-ordinates of $D.$
✓

Answer

(i) Coordinates of the points $A, B$ and $C$ are $(1, 3), (-3, -2)$ and $(3, 0)$ respectively.
(ii) Slope of AB = $\frac{-2-3}{-3-1}=\frac{5}{4}$.
(iii) Line through $C(3, 0)$ and parallel to $AB.$
$\therefore$ Slope $=\frac{5}{4}$.
$\therefore$ Equation to the line is
$y - y_1 = m(x - x_1)$
$y - 0 = \frac{5}{4}(x-3)$
$4y = 5x - 15$
This line intersects Y-axis at $D.$
$\therefore$ On solving
$4y = 5x - 15$
and $x = 0, ...$(Equation to Y-axis)
We get, $4y = -15$
$y=-\frac{15}{4}$
$\therefore$ Coordinates of point D are $\left(0,-\frac{15}{7}\right)$.

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