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.
The points A(-1, -2), B(4, 3), C(2, 5) and D(-3, 0) in that order form a rectangle.
✓

Answer

True:ABCD will from a rectangle if:
  1. It is a parallelogram.
  2. Diagonals are equal.
For parallelogram: Diagonals bisect each othere.
i. e., Mid point of AC = Mid point of BD is
$\text{i.e,}\Big(\frac{-1+2}{2},\frac{-2+5}{2}\Big)=\Big(\frac{4-3}{2},\frac{3+0}{2}\Big)$
$\Rightarrow\Big(\frac{1}{2},\frac{3}{2}\Big)=\Big(\frac{1}{2},\frac{3}{2}\Big)$
Hence, ABCD is a parallelogram.
Now, Diagonal $\text{AC}=\sqrt{(2+1)^2+(5+1)^2}$
$\Rightarrow\text{AC}=\sqrt{9+49}$
$\Rightarrow\text{AC}=\sqrt{58}\text{ units}$
and Diagonal $\text{BD}=\sqrt{(-3-4)^2+(0-3)^2}$
$\Rightarrow\text{BD}=\sqrt{49+9}$
$\Rightarrow\text{BD}=\sqrt{58}\text{ units}$
Digonal AC = Digonal BD
Hence, ABCD is a rectangle.

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

If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius $2r$, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle. Is this statement false Why?
→
Write ‘True’ or ‘False’ and justify your answer.
The length of tangent from an external point on a circle is always greater than the radius of the circle.
→
Write ‘True’ or ‘False’ and justify your answer.
If a chord AB subtends an angle of 60° at the centre of a circle, then angle between the tangents at A and B is also 60°.
→
The product of two irrational numbers is an irrational number (True/ False).
→
If a quadratic polynomial f (x) is not factorizable into linear factors, then it has no real zero.
→
The value of $\sin \theta+\cos \theta$ is always greater than 1 .
→
The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal? Why?
→
Write the truth value (T/F) of each of the following statements:
Two triangles are similar, if their corresponding sides are proportional.
→
The numerical value of the area of a circle is greater than the numerical value of its circumference. Is this statement true? Why?
→
D is a point on side QR of $\triangle\text{PQR}$ such that $\text{PD}\perp\text{QR}$ will it be correct to say that $\triangle\text{PQD}\sim\triangle\text{RPD}?$ Why?
→