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right triangle abc is on a coordinate plane. segment ab is on the line y = 2 and is 6 units long. point c is on the line x = −3. what is the y-value of point c if the area of δabc is 9 units squared?

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Choice A) 5

Explanation:

The line y = 2 is a horizontal line passing through 2 on the y axis. Every point on this line has a y coordinate of 2. Since both A and B are on this line, this means AB is horizontal as well. This can be thought of as the base of the triangle. AB = 6 is the length of the base.

We don't know the height, so we'll call that h.

We do know the triangle area is 9 square units

The formula we'll use is

area = (base*height)/2

Plug in the given values and solve for h

9 = (6*h)/2

9*2 = 6h

18 = 6h

6h = 18

h = 18/6

h = 3

The height of the triangle is 3. This means that point C is either 3 units below y = 2 or point C is 3 units above y = 2.

If points C is 3 units below y = 2, then its y coordinate would be 2-3 = -1. But this isn't an answer choice. So we ignore this scenario.

If point C is 3 units above y = 2, then this point has a y coordinate of 2+3 = 5.

Below is one possible diagram of how the triangle could look like. Point C is always fixed at (-3,5); however point A is allowed to slide around as long as it has a y coordinate of y = 2. Point B is a similar story as point A. Furthermore, segment AB must always be 6 units long.

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

Answer: d. 39 cmin the diagram, the approximate length of the minor arc de is 39 centimetres.step-by-step explanation: the formula for the length of an arc in a circle is as displayed below.let the length of the minor arc de = xx = 2( pi )r × angle of sector / 360°from this, we will substitute the values given from the problem into the formula to obtain the length of the minor arc de.x = 2( pi )r × angle of sector / 360°r = radius = 25cmpi as an approximate value = 3.14angle of sector = 120°x = 2( 3.14 )( 25 ) × 120° / 360°x = 157 × 1 / 4x = 39.25x = 39 ( rounded to the nearest whole number as an approximate value )