If ABCD Is A Square Where A(2,3), B(6,7), C(10,1), Then D=?: - Testpoint

Testpoint Whatsapp group

Testpoint Whatsapp group

If ABCD is a square where A(2,3), B(6,7), C(10,1), then D=?:

(6,3)
(-6,-3)
(6,-3)
(6,5)

Explanation

We are given three vertices of a square ABCD:
$A (2, 3)$
$B (6, 7)$
$C (10, 1)$
We need to find $D (x, y)$ .
Step 1: Understanding the Square Properties
A square has equal sides and perpendicular diagonals. The diagonals also bisect each other at their midpoint.
Step 2: Find the Midpoint of Diagonal AC
The midpoint formula for two points ( $1$ $,$ $y$ $1$ $)$ and ( $2$ $,$ $y$ $2$ $)$ is:
$M = (x _{1} + x _{2/2}, y _{1} + y _{2/2})$ For diagonal AC:
$M = (2 + 10, 3 + 1/2)$ $M = (12/2, 4) = (6, 2)$ Step 3: Use Midpoint to Find D
Since diagonals bisect each other, midpoint M is also the midpoint of diagonal BD.
Using the midpoint formula for BD:
$M = (B _{x} + D _{x} \frac{B _{y} + D _{y/2}}{2,})$ Substituting B $6$ $,$ $7$ $)$ and M $6$ $,$ $2$ $)$

$(6, 2) = (6 + D _{x}, 7 + D _{y})$

Step 4: Solve for D

Equating the coordinates:

For x-coordinate:
$6 + D _{x/2} = 6$ $6 + D_{x} = 12$ $D_{x} = 6$
For y-coordinate:
$7 + D _{y} = 2$ $7 + D_{y} = 4$ $D_y = -3$

$D = (6, - 3)$

Correct option: (6, -3)

Related MCQs

The extraction of a square root of a given number is?

دیئے گئے نمبر کے مربع جڑ کا اخراج کیا ہے؟

Binary operation
Relation
Unary operation
Relation in some set

اس سوال کو وضاحت کے ساتھ پڑھیں

What is the angle between the hands of a clock at 6:30?

0 degree
10 degree
15 degree
20 degree

اس سوال کو وضاحت کے ساتھ پڑھیں

What is the angle between the hour hand and the minute hand of a clock at 12:30?

150°
165°
180°
175°

اس سوال کو وضاحت کے ساتھ پڑھیں

A clock shows 3:40. What is the smaller angle between the hour hand and the minute hand?

130°
120°
140°
None of these

اس سوال کو وضاحت کے ساتھ پڑھیں

If point Q is 7 cm away from the center of a circle and the radius of the circle is 4 cm, then how many tangents can be formed from point Q?

2
3
1
None of these

اس سوال کو وضاحت کے ساتھ پڑھیں

Test Point Whatsapp Channel

All Rights Reserved © TestPointpk.com