# geometry

Given three collinear points X, Y, and Z and XY=8 and YZ=20, what is the length of a segment joining the midpoint XY and YZ?

1. 👍 0
2. 👎 0
3. 👁 168
1. Draw line segment XZ and let X = 0, the
starting point.

Xy = Y - 0 = 8,
Y = 8.

M1 = (8-0) / 2 = 4 = Mid-point of XY.

YZ = Z - Y = 20,
Z - 8 = 20,
Z = 28.

M2 - Y = 20 / 2 = 10,
M2 - 8 = 10,
M2 = 18.

Segment M1M2 = M2 - M1 = 18 - 4 = 14.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Math

Rewrite the following definition as a biconditional: Points that lie on the same line are collinear. A.) If a point lies on a line, then it is collinear. B.) If a point lies on a line with another point, then the two points are

2. ### Geometry

Which statement is not used to prove that ΔFGH is similar to ΔFIJ? triangles FGH and FIJ in which point I is between points F and G on segment FG and point J is between points F and H on segment FH Angle F is congruent to

3. ### math

Points​ P, Q,​ R, and S are collinear. Point Q is between P and​ R, R is between Q and​ S, and PQ overbar congruent RS overbar. If PSequals30 and PRequals23​, what is the value of​ QR

4. ### Math

Two collinear points are given in the table, give a third point that is also on this line x 0 4. It is written vertically on a graph, the other side states y 0 -3. I do not understand how to find the third point for each problem.

1. ### Maths

the points A,B,C and D lie on a straight line. The ratio of the length of AB to the length of BC is 3:4 and the ratio of the length of AC to the length of CD is 2:1. Find the ratio of the length of BC to the length of AD ?

2. ### geometry

Trisha drew a pair of line segments starting from a vertex. Which of these statements best compares the pair of line segments with the vertex? Answer A:Line segments have two endpoints and a vertex is a common endpoint where two

3. ### geometry

P, Q, and S are collinear and the measure of PQR = 120°. What does the measure of SQT have to equal to ensure that R, Q, and T are collinear?

4. ### math

For what value of 'k' the points ( -k + 1, 2k), (k, 2 - 2k) and ( - 4 - k, 6 - 2k) are collinear.

1. ### geometry

In four non collinear points , how many line segments can be drawn?

2. ### Trigonometry

1. A, B and C are collinear, and B is between A and C. The ratio of AB to AC is 3:4. If A is at (-8,1) and B is at (-2,-2), what are the coordinates of C? 2. The segment joining (1,-3) and (4,-6) is extended a distance equal to

3. ### geometry

Points A, B, and C are collinear with B between A and C. Points M and N are the midpoints of segments AB and AC , respectively. Prove that BC = 2MN.

4. ### mathematics

Ten points are marked on one side of △ABC. Another side of △ABC has 11 marked points and the third side has 12 marked points. None of the points are a vertex of the triangle. If any three non-collinear points can be the