Download App

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.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "True False[1 Marks ]" from Coordinate Geometry→Coordinate Geometry — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

State whether the following statements are true or false. Justify your answer. Point P(5, -3) is one of the two points of trisection of the line segment joining the points A(7, -2) and B(1, -5).
→
$\pi$ is an irrational number (True/ False).
→
Write the truth value (T/F) of the following statements:
Two polygons are similar, if their corresponding angles are proportional.
→
State whether the following statements are true or false. Justify your answer.
Points A(-6, 10), B(-4, 6) and C(3, -8) are collinear such that
$\text{AB}=\frac{2}{9}=\text{AC}.$
→
Write ‘True’ or ‘False’ and justify your answer.
The tangent to the circumcircle of an isosceles triangle$\triangle\text{ABC}$ at A, in which AB = AC, is parallel to BC.
→
π is an irrational number.
→
Write True or False and give reasons for your answer in each of the following.
To construct a triangle similar to a given $\triangle ABC$ with its sides $\frac{7}{3}$ of the corresponding sides of $\triangle ABC$, draw a ray $B X$ making acute angle with $B C$ and $X$ lies on the opposite side of $A$ with respect to $B C$. The points $B_1, B_2, \ldots, B_7$ are located at equal distances on $B X, B_3$ is joined to $C$ and then a line segment $B_6 C^{\prime}$ is drawn parallel to $B_3 C$ where $C^{\prime}$ lies on BC produced. Finally, line segment $A ^{\prime} C ^{\prime}$ is drawn parallel to AC .
→
Are the following statements 'True' or 'False'? Justify your answers.
If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.
→
State whether the following statements are true or false. Justify your answer.
A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.
→
In Fig. a square is inscribed in a circle of diameter $d$ and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Give reasons for your answer.
→