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Dahasolnce [82]
2 years ago
15

What are the coordinates of point B in the diagram?

Mathematics
2 answers:
Andrej [43]2 years ago
8 0
Let the cordinates of B be (x, y), then
(3(1) + x)/4 = 1.75 and (3(5) + y)/4 = 2.5
3 + x = 7 and 15 + y = 10
x = 7 - 3 and y = 10 - 15
x = 4 and y = -5

Therefore, the coordinate of B is (4, -5)
Vinil7 [7]2 years ago
6 0

Answer:  The co-ordinates of point B are (4, -5).

Step-by-step explanation:  We are given to find the co-ordinates of point B in the diagram.

From the diagram, we note that

the co-ordinates of point A and C are (1, 5) and (1.75, 2.5) respectively.

Also, the point C divides the line segment AB internally in the ratio 1 : 3.

We know that if a point P divides a line segment joining the points (a, b) and (c, d) internally in the ratio m : n, then the co-ordinates of the point P are

P=\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).

Here, (a, b) = (1, 5), m : n = 1 : 3  and  (c, d) = ?

Therefore, the co-ordinates of point C will be

C=\left(\dfrac{1\times c+3\times1}{1+3},\dfrac{1\times d+3\times5}{1+3}\right)\\\\\\\Rightarrow (1.75,2.5)=\left(\dfrac{c+3}{4},\dfrac{d+15}{4}\right)\\\\\\\Rightarrow 1.75=\dfrac{c+3}{4},~~~~~2.5=\dfrac{d+15}{4}\\\\\\\Rightarrow c+3=7,~~~~~~~~\Rightarrow d+15=10\\\\\\\Rightarrow c=4,~~~~~~~~~~~~~\Rightarrow d=-5.

Thus, the co-ordinates of point B are (4, -5).

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Answer: (c) 31    (d) 30     (e) 41     (f) 10

<u>Step-by-step explanation:</u>

NOTES about angles of a rhombus:

  1. diagonals are angle bisectors (cut the angle into 2 equal parts)
  2. diagonals are perpendicular to each other (90°)
  3. two adjacent triangles of a rhombus form an isosceles triangle

(c) Given: ∠CBD = 59°

    Per rule 2  →  ∠BEC = 90°

    Triangle Sum Theorem: sum of the angles of a triangle = 180°

∠CBD + ∠BEC  + ∠BCE = 180°

  59°  +    90°   + ∠BCE = 180°

       149°          + ∠BCE = 180°

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(d) Given:  ∠BCD = 120°

   Per rule 3  →   ∠CBD = ∠CDB

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∠CBD + ∠CDB  + ∠BCD = 180°

           2∠CBD  +   120°  = 180°

           2∠CBD                =  60°

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                            2x      = 82

                              x      = 41

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                                  10 = x

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