Triangle xyz where x(7, 2), y(-3, 8), and z(-4, 6) is dilated with a scale factor of one-fourth . where is the dilation located?
a. x’the coordinate (negative seven-fourths, one-half), y’the coordinate (three-fourths, negative 2and z’he coordinate (1, negative three-halves)
b. x’the coordinate (one-half, seven-fourths), y’the coordinate (2, negative three-fourthsand z’the coordinate (three-halves, negative 1)
c. x’the coordinate (seven-fourths, one-half), y’the coordinate (negative three-fourths, 2and z’the coordinate (negative 1, three-halves)
d. x’the coordinate (negative one-half, seven-fourths), y’the coordinate (negative 2, three-fourthsand z’the coordinate (negative three-halves, 1)

 The correct option is

(C) X coordinate (seven-fourths, one-half), Y coordinate (negative three-fourths, 2) and Z coordinate (negative 1, three-halves).

Step-by-step explanation:  Given that the triangle  XYZ where X(7, 2), Y(-3, 8), and Z(-4, 6) is dilated with a scale factor of one-fourth.

We are to select the correct location of the dilation.

We know that

if a point (x, y) is a vertex of a triangle, which is dilated with a scale factor of s, then the new co-ordinates of the vertex will be (sx, sy).

According to the given information, the scale factor of dilation is

So, the new co-ordinates of the image triangle after dilation are

Thus, the required location of the dilation is the new triangle with vertices and

Option (C) is CORRECT.

answer: cos [   arcsin (3/5) - arccos (1/2) ] =

step-by-step explanation: × = 3/5 = 0.6--> x = 36.87 and x = 180 - 36.87 = 143.13 deg

cos y = 1/2 --> y = +- 60 deg a. cos (x - y) = cos (143.13 - 60) = cos 83,13  

=

0.12

b. cos (36.87 - 60) = cos (-23.23) = 0.92