Coordinate Geometry and the Centroid - Part 5 - Find the coordinates of the centroid of each triangle

Oct 8, 2026

Uploaded by Pentious

Coordinate Geometry and the Centroid worksheet focuses on finding each triangle’s centroid from given vertex coordinates. Multiple problems list three vertices for each triangle, requiring computation of the centroid coordinates. The set also includes critical thinking items that use midpoint connections to form a smaller triangle inside the original, asking for the smaller triangle’s centroid and an explanation of what changes. Answers emphasize centroid behavior under median construction.

LanguageEnglish

CategoryExam

FormatPDF

Pages4

Reading Time10 min

AccessFree to download

Find the centroid of each triangle

Solve problems using given vertex coordinates

Critical thinking questions

Connect midpoints to form a smaller triangle

Kuta Software-Infinite Geometry Coordinate Geometry and the Centroid Find coordinates of the centroid of each triangle. 1) 3) 5) −7 −6 −5 −4 −3 −2 −1 Z −7 −6 −5 −4 −3 −2 −1 Q | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | | S | 5 | | | | | | | | | | | | 4 | | | | | | | | | | | | 3 | | | | | | | | | | | | 2 | | | | | | | | | | | | 1 | | | | | | | | | −2 −1 R 1 2 3 4 5 6 T 7 Name Date Period 2) 4) 6) −6 D−5 −4 −3 −2 −1 1 2 F 3 | L | | | | K | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | |
− | 3 − | 2 − | 1 | | 1 2 | 3 | 4 | 5 | 6 | | | | | | −1 | | | | | | | | | | | | −2 | | | | | | | | | | | | −3 | | | | | | | | | | | | −4 | | | | | | | | | | | | −5 | | | | | | | | | | | | −6
M | | | | | | | | | −7 | | | | | | | | | | | 7) | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | | | | | | U | | | | | | | | | | 1 | | | | | | | | | − | 3 − | 2 − | 1 | | 1 2 | 3 | 4 | 5 | 6 | | | | | | −1 | | | | | | | | | | | | −2 | | | | | | | | | | | | −3 | | | | | | | | | | W | | −4 | | | | | | V | | | −5 | | | | | | | | | | | 2 8) Find the coordinates of the centroid of each triangle given the three vertices. 9) C(−7, −6), B(−8, 0), A(0, 0) 10) S(0, −6), R(−10, −6), Q( 1, 0) 11) T(0, 0), U( 1, 3), V(−2, 0) 12) Y(3, 4), X(−5, 0), W(0, 0) 13) E(6, −3), D(−5, −3), C(6, −1) 14) F(−7, −3), G(−7, −5), H(−3, −3) Critical thinking questions: 15) Two vertices of a triangle are (0, 0) and 16) For question \#1, connect the midpoints of (9, 0) . The centroid is (6, 1) . Find the third each side of the triangle to form a smaller vertex of the triangle. triangle within the original triangle. Find the coordinates of the centroid of the smaller triangle. What happened and why? Kuta Software-Infinite Geometry Name Coordinate Geometry and the Centroid Date Period Find coordinates of the centroid of each triangle. 1) 3) 5) −7 −6 −5 −4 −3 −2 −1 Z (−2, 1) −7 −6 −5 −4 −3 −2 −1 Q (−3, 4) | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | | S | 5 | | | | | | | | | | | | 4 | | | | | | | | | | | | 3 | | | | | | | | | | | | 2 | | | | | | | | | | | | 1 | | | | | | | | | −2 −1 R 1 2 3 4 5 6 T 7 (~~ ~~53~~ ~~ , 43) 2) 4) 6) −6 D−5 −4 −3 −2 −1 1 2 F 3 (−1, 2) | L | | | | K | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | |
− | 3 − | 2 − | 1 | | 1 2 | 3 | 4 | 5 | 6 | | | | | | −1 | | | | | | | | | | | | −2 | | | | | | | | | | | | −3 | | | | | | | | | | | | −4 | | | | | | | | | | | | −5 | | | | | | | | | | | | −6
M | | | | | | | | | −7 | | | | | | | | | | | ( 1, −2) (− ~~ ~~13~~ ~~ , − ~~ ~~43) 7) | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | | | | | | U | | | | | | | | | | 1 | | | | | | | | | − | 3 − | 2 − | 1 | | 1 2 | 3 | 4 | 5 | 6 | | | | | | −1 | | | | | | | | | | | | −2 | | | | | | | | | | | | −3 | | | | | | | | | | W | | −4 | | | | | | V | | | −5 | | | | | | | | | | | 2 (~~ ~~43~~ ~~ , − ~~ ~~73) 8) 1 2 3 4 5 6 7 8 (3, ~~ ~~103~~ ~~ ) Find the coordinates of the centroid of each triangle given the three vertices. 9) C(−7, −6), B(−8, 0), A(0, 0) (−5, −2) 11) T(0, 0), U( 1, 3), V(−2, 0) (− ~~ ~~13~~ ~~ , 1) 13) E(6, −3), D(−5, −3), C(6, −1) (~~ ~~73~~ ~~ , − ~~ ~~73) Critical thinking questions: 15) Two vertices of a triangle are (0, 0) and (9, 0) . The

FAQs

How do you find the centroid when the three triangle vertices are given?

Use the centroid formula based on the three vertex coordinates. Compute the centroid’s x- and y-values from the listed points.

What is the centroid in the midpoint-constructed smaller triangle?

The centroid stays the same because the medians do not change when midpoints of the sides are connected.

Why doesn’t the centroid change after connecting the midpoints to form a smaller triangle?

The medians remain the same lines in the original triangle’s geometry, so the intersection point (the centroid) is unchanged.

Oct 8, 2026

Uploaded by Pentious