Point P (–4, 2) lies on the line segment joining the points A (–4, 6) and B (–4, –6). Is the following statement true or false
Solution:
Given, line segment joining the points A(-4, 6) and B(-4, -6)
We have to determine if the point P(-4, 2) lies on the line segment.
A line segment joining the point Q (x₁ , y₁) is
y - y₁ = m(x - x₁)
Where, m is the slope.
The slope of the line joining two points P (x₁ , y₁) and Q (x₂ , y₂) is
is given by m = (y₂ - y₁)/(x₂ - x₁)
Here, A(-4, 6) and B(-4, -6)
Slope, m = -6 - 6/(-4 - (-4) = -12/0 = ∞
Now, the line segment is y - 6 = (12/0)(x - (-4))
(y - 6)(0) = -12(x + 4)
0 = -12(x + 4)
x + 4 = 0 -------------- (1)
If the point P(-4, 2) lies on the line segment then it has to satisfy the equation (1),
Put x = -4 in (1)
-4 + 4 = 0
0 = 0
Therefore, the point P lies on the line AB.
✦ Try This: Check if the point P(-4, 2) lies on the line segment joining the points A (-4, 6) and B (-4, -6).
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7
NCERT Exemplar Class 10 Maths Exercise 7.2 Problem 2
Point P (–4, 2) lies on the line segment joining the points A (–4, 6) and B (–4, –6). Is the following statement true or false
Summary:
The statement “Point P(– 4, 2) lies on the line segment joining the points A (-4, 6) and B (-4, -6)” is true as the point satisfies the equation of the line segment AB
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