Given directed line segment QS , find the coordinates of R

Mathematics

1 answer:

Degger [83]2 years ago

4 0

Answer:

The answer is below

Step-by-step explanation:

The question is not complete, what are the coordinates of point Q and R. But I would show how to solve this.

The location of a point O(x, y) which divides line segment AB in the ratio a:b with point A at ( $x_1,y_1$ ) and B( $x_2,y_2$ ) is given by the formula:

$x=\frac{a}{a+b}(x_2-x_1)+x_1\\ \\y=\frac{a}{a+b}(y_2-y_1)+y_1$

If point Q is at ( $x_1,y_1$ ) and S at ( $x_2,y_2$ ) and R(x, y) divides QS in the ratio QR to RS is 3:5, The coordinates of R is:

$x=\frac{3}{3+5}(x_2-x_1)+x_1=\frac{3}{8}(x_2-x_1)+x_1\\ \\y=\frac{3}{3+5}(y_2-y_1)+y_1=\frac{3}{8}(y_2-y_1)+y_1$

Let us assume Q(−9,4) and S(7,−4)

$x=\frac{3}{8}(7-(-9))+(-9)=\frac{3}{8}(16)-9=-3\\\\y=\frac{3}{8}(-4-4)+4=\frac{3}{8}(-8)+4=1$

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Ana wrote four statements to describe circle S. Statements: AB is a diameter. ST , SP and SQ are radii. SQ = 12 cm PQ = 12 cm Ar

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Two of the four statements that Ana wrote are correct. Number 1, "AB is a diameter" is incorrect, and so is number 3, "SQ = 12 cm". AB is not a diameter because it is instead a chord. "ST , SP and SQ are radii" is correct because they are straight lines from the center of the circle to the circumference of the circle, which is the exact definition of radius. The third statemet is incorrect because since ST is a radius and it equals 6, that means all radii are equal to 6. SQ is a radius of circle S, so it should also equal 6, not 12. The last statement is correct because PQ is a diameter of circle S. By rule, the diameter is always equal to double of the radius. The radius is 6, so 6 x 2= 12.

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1 year ago

Eli needs pieces of ribbon cut into strips that are 2 1\2 feet long. The roll of ribbon is 7 1\2 feet long. Which expression cou

julsineya [31]

Answer: There are 3 strips that can be cut from the roll of ribbon.

Step-by-step explanation:

since we have given that

Length of a ribbon is given by

$7\frac{1}{2}\ ft\\\\=\frac{15}{2}\ ft$

Length of pieces of ribbon cut into strips is given by

$2\frac{1}{2}\ ft\\\\=\frac{5}{2}\ ft$

So, we need to find the number of strips that can be cut is given by

$\text{ Number of strips }=\frac{\text{Length of roll}}{\text{ Length of strip}}\\\\=\frac{\frac{15}{2}}{\frac{5}{2}}\\\\=\frac{15\times 2}{2\times 5}\\\\=\frac{15}{5}\\\\=3$