Question

lesson 26: distance, area and perimeter on a coordinate plane 6.ns.8

1. the length of segment hg is 5 units.

the length of segment gf is 3 units.
the length of segment efgh is 16 square units.

1. the vertices of a quadrilateral drawn in a coordinate plane are (-6,6) (4,6) (2, -5) and (-6, -9). what is the length of the side joining the vertex in quadrant i to the vertex in quadrant ii?

a. 2
b. 8
c. 10
d. 12

Explanation:

Step1: Identify the vertices

The vertex in Quadrant I is \((4, 6)\) (since both \(x = 4>0\) and \(y = 6>0\)), and the vertex in Quadrant II is \((- 6,6)\) (since \(x=-6 < 0\) and \(y = 6>0\)).

Step2: Calculate the distance

Since the \(y\)-coordinates of both points are the same (\(y = 6\)), the distance between them is calculated by the formula for the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) when \(y_1=y_2\): \(d=\vert x_2 - x_1\vert\).
Substitute \(x_1=-6\) and \(x_2 = 4\) into the formula: \(d=\vert4-(-6)\vert=\vert4 + 6\vert=\vert10\vert = 10\).

Answer:

c. 10