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Coordinate Geometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsCoordinate Geometry1 Mark
Question
State whether the following statements are true or false. Justify your answer.
Point P(-4, 2) lies on the line segment joining the points A(-4, 6) and B(-4, -6).
✓

Answer

True:We observe that x-coordiante is sane i.e, equal to (-4) so line is parallel to y-coordinate of P i.e., 2 lies between 6 and -6 of A and B respectively. Hence, P lies between and on AB.
Alternate Answer
Point P(-4, 2) will lie on the line AB if area of $\triangle\text{ABP}$ is Zero.
$\therefore\text{i.e., } \text{ar }\text{ABP}=0$
$\Rightarrow\frac{1}{2}\big[\text{x}_1(\text{y}_2-\text{y}_3)+\text{x}_2(\text{y}_3-\text{y}_1)+\text{x}_3(\text{y}_1-\text{y}_2)\big]$
$\Rightarrow\frac{1}{2}\big[-4(-6-2)-4(2-6)-4(6+6)\big]=0$
$\Rightarrow\big[-4(-8)-4(-4)-4(12)\big]=0$
$\Rightarrow32+16-48=0 $
$\Rightarrow48+48=0$ which is true.
Hence, point P lies on the line joining A and B.

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