NRICH: Graph Triangles

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NRICH: Graph Triangles

Use the information about the triangles on this graph to find the coordinates of the point where they touch.

This is the graph of the line y=−2x+12.Diagram showing the graph y=-2x+12. A point P on the line divides the segment in the positive quadrant into two segments. The upper segment determines a blue triangle by drawing the line parallel to the x axis, and the lower segment determines a red triangle by drawing the line parallel to the y axis.

Point P is on this line.

The ratio of the area of the red triangle to the area of the blue triangle is 1:4.

Find the coordinates of point P.

This problem is adapted from the World Mathematics Championships

You can find more short problems, arranged by curriculum topic, in our short problems collection.

Ages 14 – 16

NRICH (University of Cambridge)
Math Topics
Algebra & Pre-Algebra, Functions & Graphs, Linear Equations
High School, Educator
9th Grade, 10th Grade, 11th Grade
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NRICH: Graph Triangles

Use the information about the triangles on this graph to find the coordinates of the point where they touch.

This is the graph of the line y=−2x+12.Diagram showing the graph y=-2x+12. A point P on the line divides the segment in the positive quadrant into two segments. The upper segment determines a blue triangle by drawing the line parallel to the x axis, and the lower segment determines a red triangle by drawing the line parallel to the y axis.

Point P is on this line.

The ratio of the area of the red triangle to the area of the blue triangle is 1:4.

Find the coordinates of point P.

This problem is adapted from the World Mathematics Championships

You can find more short problems, arranged by curriculum topic, in our short problems collection.

Ages 14 – 16

NRICH (University of Cambridge)
Math Topics
Algebra & Pre-Algebra, Functions & Graphs, Linear Equations
High School, Educator
9th Grade, 10th Grade, 11th Grade

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NRICH (University of Cambridge)

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