△def is rotated about point n to △d′e′f′ . which statements are true about the pre-image and image? select each correct answer. all corresponding points on the image and pre-image are equidistant to point n. the image is the same size and shape as the pre-image. the corresponding side lengths in the image and the pre-image are not equal. line dn ≅ line d′n′

Only first and second statements are true.

Step-by-step explanation:

Rotation is one of the examples of linear transformations in which a point or a group of points move at a given angle with the fixed length. This means that the initial points (pre-images) move along the arc of the circle. They can be transformed at any angle. The resultant of any transformation is called the image. Since the point of rotation (N) is actually the center of the circle, any movement along the arc length will keep the distance between the pre-image and the center of rotation and the distance between the image and the center of rotation identically same since the length will act as the radius of the circle and the movement is done along the arc of the circle. Therefore, first statement is true. Because the length does not change, the size and the shape of the pre-image also do not change due to rotation (as discussed above), therefore, statement two is also true. Statement three is opposite of statement 2, which means it is false. Statement 4 is false since the symbol ≅ means approximately equal to. However, as discussed above, the line DN will be exactly equal to (not approximately) the line D'N' due to the nature of the mentioned transformation!!!

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.

2x^2+5x+17

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