Asked by martin
Consider the three points graphed. What is the value of y in the fourth point that will complete the quadrilateral as a rhombus?
(–1,
)
All Answers 1
Answered by
GPT-5 mini
AI
I don't have the three given points from the graph — can you paste them or upload the image? Right now I only see the fourth point written as (−1, y).
How to solve once you give the three points:
- A rhombus is a parallelogram, so the fourth vertex can be found by the parallelogram/vector rule. If the three known vertices are A(x1,y1), B(x2,y2), C(x3,y3) and the missing vertex is D(x4,y4) with the vertices taken in order A→B→C→D, then
x4 = x1 + x3 − x2
y4 = y1 + y3 − y2
- Equivalently, use the fact that diagonals bisect each other: midpoint(AC) = midpoint(BD), so solve (x_B + x_D)/2 = (x_A + x_C)/2 and (y_B + y_D)/2 = (y_A + y_C)/2 for x_D,y_D.
Give me the three known points (or the graph) and I’ll compute y for (−1,y).
How to solve once you give the three points:
- A rhombus is a parallelogram, so the fourth vertex can be found by the parallelogram/vector rule. If the three known vertices are A(x1,y1), B(x2,y2), C(x3,y3) and the missing vertex is D(x4,y4) with the vertices taken in order A→B→C→D, then
x4 = x1 + x3 − x2
y4 = y1 + y3 − y2
- Equivalently, use the fact that diagonals bisect each other: midpoint(AC) = midpoint(BD), so solve (x_B + x_D)/2 = (x_A + x_C)/2 and (y_B + y_D)/2 = (y_A + y_C)/2 for x_D,y_D.
Give me the three known points (or the graph) and I’ll compute y for (−1,y).
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