Which of the following is being constructed in the image.
1. a line parallel to a given line through a point not on the line
2. a perpendicular bisector of a line segment
3. a line perpendicular to a given line through a point not on the line
4. a line segment that is congruent to a given line segment

This is about construction of lines.

The correct answer is option 3; A line perpendicular to a given line through a point not on the line.

Then one leg of compass is placed at each point with a fixed distance and another small arc is drawn which we can see to the right intersecting each other.

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  3. a line perpendicular to a given line through a point not on the line

Step-by-step explanation:

The point not on the line suggests that choices 1 and 3 are possibilities. The fact that the dotted line is not parallel (and is perpendicular) to the solid line suggests that choice 3 is applicable and choice 1 is not.

The short arcs are equidistant from the end points of the chord that intercepts the larger arc. Hence the line through the crossing point of the short arcs and the point on the other side of the line will be the perpendicular bisector of the chord, and will be perpendicular to the solid line. Creating that perpendicular is likely the purpose of the construction.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15