Q10 of 112 Page 156

The line joining the points A (–2, 3) and B (a, 5) is parallel to the line joining the points C (0, 5) and D (–2, 1). Find the value of a.

Line joining points A (–2, 3) and B (a, 5) IA parallel to the line joining the points C (0, 5) and D (–2, 1)


The two lines are parallel only when their slopes are equal.


∴ slope of AB = slope of CD


Slope of line passing through (x1, y1) and (x2, y2) is



Slope of AB is:


A (–2, 3) and B (a, 5)




Slope of CD is:


C (0, 5) and D (–2, 1)





As per the property, the two lines are parallel only when their slopes are equal.


i.e. Slope of AB = Slope of CD


⇒


⇒ 2 = 2(a + 2)


⇒ 2 = 2a + 4


⇒ 2a = 2 – 4


⇒ 2a = –2


⇒


⇒ a = –1


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