Question

9. A and B are two points with coordinates (4, 1) and
(10, 1), respectively. Find two pairs of points C, D
and P, Q in the first quadrant such that ABCD and
ABPQ form parallelograms, each with height 4 units
and perimeter 22 units.​

Answer 1

Step-by-step explanation:

Distance between A and B = |4 - 0| = 4

Since the opposite sides of a parallelogram are equal, the distance between C and D is also 4.

Also, the y-coordinates of A and B are equal, the side AB is parallel to the x-axis. And, since ABCD is a parallelogram, CD is also parallel to the x-axis. So the y-coordinates of C and D are also equal.

Thus, the x-coordinate of D = 8 - 4 = 4

Hence, the coordinates of D are (4, 5).

(b) The x-coordinates of D and B are equal. So the line BD is parallel to the y-axis or BD is perpendicular to the x-axis.

So, height of the parallelogram =DB=∣y1−y2∣=∣5−2∣=∣3∣=3

(c) BC=(x1−x2)2+(y1−y2)2

=(8−4)2+(5−2)2

=(42)+(3)2

=16+9

=25

= 5 units

AD = BC = 5 units

Perimeter =2×(4+5)=18 units

Area=Base×Height=4×3=12sq.units

Answer 2

Answer:

12sq

Step-by-step explanation:

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