Point y is the circumcenter of triangle d e f. lines are drawn from the points of the triangles to point y. lines are drawn from point y to the sides of the triangle to form right angles and line segments y l, y m, and y n. the line segments cut the sides of the triangles into 2 equal parts. which statement is true about point y?
a) point y is the center of the circle that passes through points d, f, and n.
b) point y is the center of the circle that passes through points m, n, and e.
c) point y is the center of the circle that passes through points l, m, and n.
d) point y is the center of the circle that passes through points d, e, and f.

Point Y is the center of the circle that passes through points D, E, and F.

Step-by-step explanation:

If we draw a circle through all the vertices of a triangle then the circle obtained is the circumcircle of the given triangle.

And the circumcenter is the center point of the circumcircle which is obtained by the point of intersection of the perpendicular bisector of all the sides of the triangle.

Therefore, since Y is the circumcenter of the triangle DEF, so, point Y is the center of the circle that passes through points D, E, and F. (Answer)

a = 11 : 4

b = 38

c = 1 for every 6

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.