Question

According to medical science and research, keeping an aquarium in the house

helps in treating stress, anxiety and health problems associated with blood

pressure. It also provides visual stimulation and creativity. A sketch of an

aquarium is drawn which is given in the following figure.

Considering P as the origin, answer the following questions:

1. The coordinates of G are

(A) (4, 9) (B) (8, 4) (C) (9, 4) (D) (8, 4)

2. The distance of the point A from the x axis is

(A) 4 units (B) 5 units (C) 6 units (D) 7 units

3. The length of the diagonal FD is

(A) √15 units (B) √61 units (C) 8 units (D) √8 units

4. The midpoint of HG is

(A) (5.5, 4) (B) (11, 4) (C) (6.5, 8) (D) (8, 4)

5. If Q is considered as the origin, then the coordinates of the midpoint of BC

are

(A) (4, 1) (B) (2, –4) (C) (–2, 4) (D) (–1, 4)


PLEASE HELP ME FAST!!!!!!!

Answer 1

Answer:

According to medical science and research, keeping an aquarium in the house

helps in treating stress, anxiety and health problems associated with blood

pressure. It also provides visual stimulation and creativity. A sketch of an

aquarium is drawn which is given in the following figure.

Considering P as the origin, answer the following questions:

1. The coordinates of G are

(A) (4, 9) (B) (8, 4) (C) (9, 4) (D) (8, 4)

2. The distance of the point A from the x axis is

(A) 4 units (B) 5 units (C) 6 units (D) 7 units

3. The length of the diagonal FD is

(A) √15 units (B) √61 units (C) 8 units (D) √8 units

4. The midpoint of HG is

(A) (5.5, 4) (B) (11, 4) (C) (6.5, 8) (D) (8, 4)

5. If Q is considered as the origin, then the coordinates of the midpoint of BC

are

(A) (4, 1) (B) (2, –4) (C) (–2, 4) (D) (–1, 4)

Answer 2

Step-by-step explanation:

Given: According to medical science and research, keeping an aquarium in the house helps in treating stress, anxiety and health problems associated with blood pressure. It also provides visual stimulation and creativity. A sketch of an aquarium is drawn which is given in the figure attached.

To find: Considering P as the origin, answer the following questions:

1. The coordinates of G are

(A) (4, 9) (B) (8, 4) (C) (9, 4) (D) (8, 4)

Solution:

See the attached figure and mark numbers on the x-axis and y-axis.

To find coordinates of G, count the line of/check the number of x-axis and then y-axis.

It is 9 and 4 respectively.

Thus,

Coordinate of G is (9,4)

Option C is correct.

2. The distance of the point A from the x axis is

(A) 4 units (B) 5 units (C) 6 units (D) 7 units

Solution: Distance of any point from x-axis is its y- coordinates and vice versa.

Thus,

According to part 1, coordinate of A is (4,6)

So,

Distance of point A from x-axis is 6 units.

Option C is correct.

3. The length of the diagonal FD is

(A) √15 units (B) √61 units (C) 8 units (D) √8 units

Solution:

Distance formula: If P(x1,y1) and Q(x2,y2) are two points,then

$\bf PQ = \sqrt{( {x_2 - x_1)}^{2} + ( {y_2 - y_1)}^{2} }$

In order to find distance FD, first write the coordinates of F and D.

F(9,8)

D(4,2)

$FD= \sqrt{( {9 - 4)}^{2} + ( {8 - 2)}^{2} }$

$FD= \sqrt{ {5}^{2} + {6}^{2} }$

$FD= \sqrt{25 + 36}$

$FD= \sqrt{61} \: units$

Option B is correct.

4. The midpoint of HG is

(A) (5.5, 4) (B) (11, 4) (C) (6.5, 8) (D) (8, 4)

Solution:

Mid-point formula: If P(x1,y1) and Q(x2,y2) are two points,than mid-point(M) is given by

$\bf x = \frac{x_1 + x_2}{2} \\ \\\bf y = \frac{y_1 + y_2}{2}$

Write the coordinates of H and G.

H(2,4)

G(9,4)

Mid-point of HG is

$x = \frac{9 + 2}{2}$

$x = 5.5$

$y = \frac{4 + 4}{2}$

$y = 4$

Mid-point of HG is (5.5,4).

Option A is correct.

5. If Q is considered as the origin, then the coordinates of the midpoint of BC are

(A) (4, 1) (B) (2, –4) (C) (–2, 4) (D) (–1, 4)

Solution: If Q is considered as origin, then coordinates of B(-1,6) and C(-1,2), because on left side of origin negative x-axis lies.

Apply mid-point formula:

$x = \frac{ - 1 + ( - 1)}{2}$

$x = \frac{ - 1 - 1}{2}$

$x = - 1$

$y = \frac{6 + 2}{2}$

$y = 4$

Mid-point of BC is (-1,4).

Option D is correct.

Final answer:

1) Option C is correct.

2) Option C is correct.

3) Option B is correct.

4) Option A is correct.

5) Option D is correct.

Hope it will help you.

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